>>709 (OP)
Thanks for your thoughtful and inquisitive post. I'll throw in my two cents while trying to keep more or less within the framework presented in the OP.
Points were already made about the politics of the everyday (at the workplace mostly), and I think it's here where we can find a path to more sophisticated engagement in politics, through the different "levels" you identified.
<1> Carrot and stick feedback
So people already engage in politics whether they realize it or not. The price of consumer goods is pretty often understood as reflecting some political situation, for example. So people already are engaged at least at this level, since their conditions are affected by politics (even if they don't meaningfully respond). Typically the way that people start acting is when their conditions noticeably worsen. However, political actors can motivate large movement by offering the "carrot" to people. This includes politicians offering some beneficial programs, unions offering to bargain for better pay, or organizations like activists and mutual aid groups working on directly solving problems. It's both possible and common to go to the people with a positive political program. That provides the opportunity for them to become more active themselves and/or to become more politically aware. Once people have the direct experience that engagement at this level can make their situation better, a lot of them are open to moving to a more sophisticated understanding.
<2> Moral consensus
Part of the task of a political movement is to build a culture. In that process, you create a set of norms and values. That's more or less the basis in our social nature on which we can build an organization that is both functional and durable. When people have that kind of shared understanding, they are much more prone to stick together despite (high-level theoretical) differences. That has been, IMHO, a major weak point of socialist organizing in the past. Political involvement is often seen as merely a hobby, because for many it is merely a hobby. As Marx predicted, the radical potential of the workers would arise not simply out of the immiseration of the workers (stick) nor the intellectual advancement (principle), but out of the forging of a new social fabric in the industrial centers, where workers would be concentrated into a mass of people with common interests and common experiences, who tend toward organizing because of the solidarity that formed between them. Before they recognize abstract ideas like the nature of wage and profit, they first recognize shared sentiments with their fellow workers and shared antipathy towards the employer. This is an important step, one that is frequently overlooked. And it's here that I think it becomes apparent that political engagement exists mainly in a hierarchy. The higher level of abstraction and principle is of critical importance, but it rests on these lower levels or else it deviates, unmoored from its connection to the people or sometimes even reality. That is, historically, how the movement has splintered into opportunism.
<3> Principled ethics
In the process of organizing people for political action, education is of great importance. This is true both in the immediate, practical sense (how do we go about effecting change?) and in the broader theoretical and historical sense (where are we going with this?). Once you have people who are motivated by interest (carrot and stick) and "part of the team" (moral consensus), you can much more readily build and understanding based in a bona fide political theory. After some involvement in the struggle it will naturally become apparent that strategizing and theorizing is important to success. Victories my be won without this, but they are less likely and more costly. In a typical organization, however, you will usually have theoretical understanding at least within the leadership. There are likely members and associates at various levels of engagement, with an intentionally developed process for guiding people to the "higher levels." This functions best in combination with waging struggle for improving workers' conditions, because it allows them more opportunity for self-development, including political development. This is how you build a revolutionary organization, anyway.
There are of course some pitfalls to the above, ways that any of these levels of engagement can be disrupted or derailed, particularly if the others are missing or weak. Which ones can you identify and how could they be defended against?
>How would you approach this issue without just A. giving everyone a vote and trusting that there will be some golden mean (doesn't work), B. calling for an uprising or a dictatorship or C. demanding handouts?
< giving everyone a vote
A revolutionary organization is self-selecting, so anybody who is a dues-paying member or equivalent is already going to be engaged at a "higher level" than normal. That may or may not be enough. Some organizations reserve some or all decision making for the leadership a la vanguardism. That's likely overkill in most situations, and involvement in decision making at a "lower" level of engagement can work well as a part of one's political education. That's not just voting either, but the other parts of the process as well, from drafting the decisions to debating and deciding what to vote on. The more involved people get, the more inclined they will be towards engaging at a "higher level" to keep up with the process and their peers. In a socialist society political education is a high priority, so that the people can exercise political power effectively and keep the movement alive.
< calling for an uprising or a dictatorship
While it's most likely inevitable that a revolutionary uprising will occur, you are correct that it is pointless to simply demand this here and now. And of course, "dictatorship" or any similar style of rule is generally disfavorable to the people and arguably antithetical to socialist development (if there is a ruler, they are usually disinclined to allow the intellectual development of their subjects). Sometimes socialists will speak of a "dictatorship of the proletariat" which is something quite different from simply a (nominally) communist party in power. It uses an archaic meaning of the word and refers to a transition period where the working class exercises political power to transform society by assuming control, in place of the capitalist class, who presently rule through a "dictatorship of the bourgeoisie."
< handouts
One of the most emphatic points to be made about socialism is that the wealth of society comes from labor to begin with, mainly that of the toiling masses. By this token, it is ours by "right." Rather than simply offering welfare through redistribution, the point is to give people a share of the value they are creating, and an understanding of it as such. There is much greater pride in that social wealth when you understand your contribution to it, and when you actually have a say in what is done with it (as opposed to your employer taking most of it to do with as they please). This reconfiguring of production and material wealth is one of the great attractors to socialism, and can be found presently in many working class organizations now, whether they are revolutionary or not. It's a mode of production and distribution that people find favorable, and what people tend to default to in social contexts without an imposed class structure.