Sisiutil said:
I could switch right now and take the overflow with me. Should I just bee-line to the UN, via Electricity -> Radio -> Mass Media?
Yes, you should. That's my only quibble with the last round. Assuming you go for a diplomatic win, researching Communism and Railroad isn't really going to gain you anything. You don't really need the extra production, and you shouldn't have time to take much advantage of it anyway. Just get it over with and put these guys out of their misery. You're in the home stretch now.
As far as switching to Universal Suffrage, you could probably do it without losing Cyrus (he would drop to +9 which is 2 more than the minimum value you need), but the more important point is that you really don't need to make that switch. At this point, only four things should be on your radar: research Electricity, research Radio, research Mass Media, build the UN. Universal Suffrage isn't going to help significantly with any of those. If Frederick overtakes Napoleon, then you almost definitely want to be in Representation, since you'll probably need every point you can find to swing Cyrus over to your side.
Patagonia's idea of gifting Biology for peace is brilliant. Terribly risky but brilliantly devious at the same time. Don't necessarily take that as an endorsement. I think it could easily backfire, and it probably isn't necessary, but it's certainly a fine example of some out of the box thinking.
Let's do some quick back of the envelope calculations on how the vote might go. You have 40% right now, which if you build lots of farms and focus on growth (set all your new Egyptian cities to emphasize food) should easily grow to 45% before the vote. It might go higher, but 45% is certainly within reach. Napoleon has 20%. That leaves 40% at the moment distributed between Frederick, Cyrus, and Washington. Mostly Frederick and Cyrus.
Since Washington is nearly irrelevant, the bad news is that means Frederick and Cyrus are probably very, very close to Napoleon's 20%. The good news is that you're only 22% away from victory. Some farm-fueled growth and either one of Frederick or Cyrus should be enough to get you the win, especially if Washington also throws a few votes your way.
So what's the conclusion?
- hurry up and win before Napoleon falls behind!

- build farms in any city where you can afford to do so. That means any city that isn't a top science or production city. At this point you can afford to farm over some cottages. Prioritize the smaller cities, because they'll grow faster.
- maintain excellent relations with Frederick and Cyrus, especially Cyrus if we assume that Frederick is #3 in population. Check the Cyrus -> Frederick attitude to see if there's anything you can do to sour their relationship. Maybe you can bribe Cyrus to switch religions or civics. Consider some resource or technology gifts to Cyrus if it's a close call.
- don't neglect Washington. His votes could make the difference, and he's so backward that you can gift him almost anything without risk (though keep Biology if possible to prevent him from trading it to the others).
edit: 1 additional point re: Washington -- don't build up culture to pressure Seattle. You don't need it, and the close borders can only hurt you. Don't avoid culture in the nearby cities. Whatever happens naturally happens, but don't go out of your way to try to steal it from him. It's a pointless city.