Conquest Victory with 77 Turns remaining in the game!
As per the plan, it was Conquest or bust. I had all of the Spaceship Parts minus 1, I had 2 Legendary Cities and had a Great Artist to be able to give me enough Culture for a 3rd Legendary City, I was hovering under the Domination Land Area Limit, and I could have easily voted myself into a UN Victory. Yet, none of those Victory Conditions really interested me.
Instead, I did everything that I could to wipe Toku and Brennus off of the map. Brennus offered me a Permanent Alliance, but I refused to take it. Wow, that was a clever setup, DynamicSpirit, with Toku being an AI who apparently won't offer a Permanent Alliance.
I didn't even try to take either AI as a Peace Vassal; in hindsight, I wonder if doing so would have been possible. Maybe Toku will equally be unwilling to be a Peace Vassal? I'm not sure, as by the time that I thought to look, both AIs felt that I was Too Powerful for them to join me as either a Permanent Ally or a Peace Vassal. I think that the real reason for the refusal has to do with total Land Area and total Population being above certain thresholds (50%?) for the map, and that refusal reason seems to take priority over saying that one is not Friendly enough, as I believe was Toku's reason for not being willing to form a Permanent Alliance earlier on in the game. Since you can't get above a Friendly relationship with Toku (or with any AI, for that matter), it means that he won't accept a Permanent Alliance with you or with any player, so that fact meant that Brennus and Toku wouldn't have shut us out of the possibility of getting a Permanent Ally by Permanently Allying with each other instead of with us.
I focused on grabbing the Religions and early-game Wonders while also focusing on expansion. Doing so cost me a blocking City early on which I was able to resettle 2 turns ahead of Toku getting to that area, but it also meant Toku and Brennus breaking through my blockade of Cities and getting 3 more troublesome Cities for me to Culture Flip later.
In total, I believe that I had to Culture flip 5 of Toku's Cities and 6 of Brennus'.
I suppose that another way to have played the map would have been to have let the enemies overrun our allies, but at least in my game, the enemies were quite incompetent and their lands got so heavily pillaged by my allies (my War Chariots were also to blame, heh heh) that the enemies really didn't pose enough of a threat to go with that route.
Perhaps if I'd settled only a couple of Cities on the mainland and then settled all of my other Cities on islands, there would have been a chance to let my allies dies off via warfare, but I enjoyed the Culture Crush challenge.
As a game highlight, let me show you the most difficult City to Culture Flip. Garrisoning a City with Military Units is highly effective at stopping a City from Revolting. A City will Culture Flip on its second City Revolt, except for in a few cases. But, if the garrison is sufficiently large, you will have a 0% chance of that City going into Revolt and therefore that City will not be able to Culture Flip.
Through the use of carefully-planned City-gifting (Cities that our enemies would be able to hastily recapture), I "encouraged" Brennus to siphon off 2 of his Military Units at a time. His Military Units would head out to garrison the newly-received City, only to find that the City got recaptured by an enemy AI before his forces could arrive to defend the new City... well, sometimes. I actually had Brennus effectively guard 3 of the gifted Cities and then I had to spend a good number of turns trying to "encourage" the enemy AIs to capture those Cities as best as I could.
A couple of turns before Brennus' last core City Culture Flipped to me, it had these odds of his last core City going into a City Revolt:
Fortunately, early on in the game, I'd had my first City Revolt in that City, so as soon as this City went into Revolt, it became mine, due to it being the second time that the City went into Revolt from the same player's Culture (my Culture). From there, I just had to wait until the AIs finished off the last of the Cities gifted to Brennus.
It was satisfying that Monte's 0.1-Health Trebuchet was the Military Unit to finish off Brennus' last City, with Brennus having an Axeman and a Longbowman being 1 turn away from garrisoning said City! :0
Meanwhile, I was spending, I believe, 90 Gold per turn to sabotage the 1 Hammer that Brennus kept putting into an Archer in that City, just to prevent him from whipping the Archer in said Size-2 City on the following turn... for about 5 turns in a row.
I'd previously had Military Units outside of every AI City, but I'd had to pull many of my forces back just to get the enemy AIs to go after Brennus' Cities. So, then it was a race to finish off those AIs in the next 2 turns, using help from Nukes, 4-movement-point Gunships (aka helicopters), and a few amphibious assaults to get the Cities without enough ground troops nearby to be able to take the Cities sooner than 4 to 5 turns.
Thank you for a fun game with a well-thought out challenge!
Should look into that. 
How many culture bombs did you use? Very clever about luring out the garrisons. And please remind me under what circumstances you can see AI city screens?
