SO, do this to vote for full-time legislators. There could be a tree of proxy voting, where some folks proxy with a trusted relative, their minister or a local politico. They could vote their bloc on up the food chain, until somebody wins say 1M votes - they become a legislator?
Isn't this more or less how the current system works? At least in the UK, it is allowed to nominate someone to vote on your behalf in a general election. The only difference is that candidates have to choose to stand for election under the current system and it seems unfair to vote someone into a political office if they don't want it!
Unfair perhaps, but I have a hunch that such people would make much better politicians than those who seek power. I'd even suggest that this could be the definition of citizenship: if you want to be a citizen (and vote), then you need to be willing to accept that you might be elected to serve.