"so, here's something that's been kicking around my head lately."
Very glad to know that you've been thinking on these questions. Far too many people simply accept the status quo and do NOT question.
"Voting, especially in America, is the only thing that (sometimes) gives us power over our representative government."
There are at least 3 assumptions here:
First, voting does NOT equate with power. Voting is merely sending a signal, a method of providing information by indicating the preference of the one(s) doing the voting. (Those who are eligible to vote and purposely not doing so are also sending a message, but I'll get to that later.) It could be a vote cast in favor of a person to receive a particular award or position; it could be a vote to approve or disapprove some proposed measure to be taken by a group of which the voter is a member. But in no way does sending that message - casting a vote - enable the voter to do *anything* more than wait and see what happens (but then that also happens for all who did not vote) while saying that they voted.
The "us" and "our" are plural pronouns and if an individual is merely signaling his/her preference, the fact that more than one individual is also signaling and even sending the same signal does not change the fact that voting is still just an individual sending a signal/notice/information. Even when the majority of some group send the same message - vote in the same manner on the same question/candidate - the individual voters have not gained any "power". (They have not all chosen to not associate with some person or group for whatever reason - eg. unacceptable behavior/prices - which would be a negative physical action of power having both a direct physical effect - reduction of the available actions of the parties - and sending a strong message.) As long as the individuals are rule-abiding members of the group, by choice or compulsion, they cannot do anything more than the rules of that group permit. (The overriding "group" currently is the government which has claimed jurisdiction where an individual happens to be, and in the case of the USA, simply was born or otherwise obtained citizenship even if no longer living there.)
Members of a government (not "representatives" in the vernacular meaning, since they have no contractual obligation to do anything) do have some semblance of "power"; they create words - lots of them - describing what they want the government enforcers to require others to do. Sure, most political representatives pay some attention to what voters "say" by way of votes and other signaling methods; they want to stay in their positions of influence and "power". However, government representatives only have "some semblance of power" because, these politicians - whether they be in the legislature, executive or judiciary - do NOT get out into the cities/towns/rural areas to physically force the people to obey the millions of words they have passed/signed/reviewed into laws/regulations/edicts/mandates/rulings/etc each year alone. The actual power is held by the government enforcers - individuals quite willing to threaten and actually initiate physical force on others. These enforcers have been given "legal authorization", thereby somehow making the initiation of physical harm socially acceptable.
"When that government, however, becomes as abusive and non-representative as ours has become, should we as a populace boycott voting? And at what point do we recall our consent and start a new system of government?"
The US government - and we are referring to it, though people everywhere can ask the same question of the government that claims jurisdiction in their locale - most definitely has been abusive to the residents of the US (and elsewhere) for a very long time. And quite a number of individuals have publicly stated their assessment of that for a very long time (Lysander Spooner, Henry David Thoreau, Benjamin Tucker to name just a very few going back quite a ways). What makes the current time different IMO is that the technology, for the past 10 years at least, has enabled very large numbers of people to become aware of what is currently going on in the country (and around the world) in increasingly real-time. Seeing videos of the activities of government enforcers (covert and overt) at home and abroad initiating physical harm is something that few people will ignore. Some will be convinced that the government has acted appropriately, but increasingly more are not so convinced, especially when they read/listen to those at the receiving end of the harm.
Voting has long been assessed by those who are opposed to government as granting approval to the system; that by joining in on the process, one signals that it approves of the idea that government, which only exists by virtue of the physical force threatened/used by its hired enforcers, is entitled to use those enforcers to carry out the programs it devises. This is the view I have come to agree with in the past 11.5 years. The only time I think that a government-related vote is appropriate is on a referendum when there is the opportunity to directly vote for less government/taxes; this I've done once since my last typical citizen voting in 1998.
Boycotting voting - or even casting votes for "none of the above" or "abolish the office", if such choices were available in a representative election - would be sending a totally different message than that of simply voting for the least objectionable candidate. When accompanied by public statements of dissatisfaction with the current system (even if not fully formulated) as for why one is NOT voting, it is then clear that the person is not simply "too busy".
The mainstream media pays little attention to actual voter turnout in the US; it was less than 39% of voter age population in 2010, lower than most people likely think. And there is no increased enthusiasm in voting predicted for this coming election in a Presidential election year. Consider the effect of many people publicizing this information on the Internet as part of a movement encouraging purposeful voter boycott. Instead of promoting "democracy" - the idea that the majority should decide what the minority and all of themselves should be legally allowed to do - promote the idea that social order can occur without government. This necessitates that a large number of people - but not necessarily the majority initially - come to understand and agree with the principles that enable a self-ordering society. This is NOT a "new system of government", but rather a totally new system of social order on a large scale; having some similarity - though not identical - to what has occurred in small villages in various parts of the world, but with the Internet now applicable to much larger areas and number of people.
"Also, how to do that via the electoral system (since any other method will likely lead to violence), if possible?"
Voting for a government is to vote for a physical harm-causing system, since governments are by their very nature employers of physical force threateners/initiators.
Society (in the US and anywhere on earth), just like any other natural system, can be naturally self-regulating by means of interactions between its members - if only humans seek to discover and are allowed to implement the methods by which such self-regulation can be effective, rather than continuing to embrace social systems that need to be constantly held in an unnatural (and very unoptimal) state of balance by the operations of their rulers and other influencers. "Social Meta-Needs: A New Basis for Optimal Interaction"
So my recommendation is to encourage young people (those under 35 are less likely to have closed their minds to new ideas) to realize that government, no matter who the candidates or whatever political party, will simply bring more of the same conditions or likely even worse. Read what I and Paul (the chief theoretician) have written related to Social Meta-Needs and implementation - and encourage others to do the same. Ask questions, make comments (noting them down as you read) and then present them in public - using quotes from the various read items - so that others can profit from the discussion. (I recommend MoreLife Yahoo for this discussion since inline responses are easily enabled there.
Along the way I would very much like to find one or more individuals who are in the process of or already have developed the skill to creatively write and, once they understand and agree with the goal Society defined in the above linked treatise, want to describe it in a fictional setting so that many more can envision it for themselves. The goal Society could also be depicted in a video game once a novel is written and available.
How to achieve this goal Society is: gradually, through convincing others - by direct reasoned logic, personal behavior example and/or Social Preferencing - that it is the only way that people should interact because it has the greatest likelihood of enabling each person to maximize his/her lifetime Happiness, the goal of each person's life whether or not s/he recognizes it.
Here is an afterthought by Paul Wakfer (my partner in all), a method that should be able to be implemented within the current electoral process and yet might have a very powerful strategic effect on the current situation.
Some highly trusted person eligible to hold the office runs for the office and pledges (AFAIK currently no actual binding contract to such effect is legally possible) to do the following, if elected.
A person running (privately funded, of course) on the above "platform" and receiving votes - even if not elected - will send a definite message to everyone: Government has got to go!
NOTE: This entire message (with very slight differences in formating) was first made public at Facebook in the Note feature on my account, but which I deleted as part of the actions taken described in the "Basic Information About You" section, not viewable by the public. However the actions of which the deletion was part were the catalyst for "Social Networks - Freedom Enhancers or Internet Ghettos?".