So, rather than getting bogged down in procedural discussion, how about my favourite thing, compromise?
This turn, I'm sure that those who would rather vote wouldn't object to supporting proposals by two players (as opposed to two by the same player); everyone has plenty of ideas, and it shouldn't be hard to find ideas by different players that are harmonious. Those who want equal division of accepted proposals surely won't insist on following chronological order, as their goal is for things to be equal over the long-term.
You can keep track of how many proposals each player has had accepted. In subsequent turns, greater weight can be given to those who are underrepresented, but with a bit of flexibility- leaving room for a key proposal by Player A to be accepted, even if Player B is one behind, with the understanding that Player B will receive even greater consideration next turn.
I'm sure everyone is interested in having fun together, and won't insist on locking some players out; conversely, I'm sure everyone will be willing to take the desires of the team as a whole into account, and won't insist on going off on a wild tangent which won't match the general strategy.
If it turns out that it really isn't possible for folks to divide their votes equitably... well, hopefully that won't happen, but let's deal with that at the time. Trying to agree on a strict system that might not prove necessary is just a needless distraction at this point.