You know it sounds a lot like Moaf's Cultural Capitals when put that way
In fact back then I suggested something along similar lines in his topic: to have different kinds, not just "cultural" capitals. It would be something new though, not aimed at a particular strategy (and maybe too dependent on location).
it would be easy to manipulate the cultural growth of the third city at this point in a normal game, and one could time out its growth
No and yes. I just observed that a city cannot grow more than one level per turn, even when producing much more culture (I hereby declare this an intended feature). The overflow is kept, but it just keeps on accumulating. So you can't get a city to legendary quickly. But it is very predictable when it will achieve the status.
maybe a system of diminishing returns to make each city after the first harder would work.
As the speed of going legendary is capped, the cities after the first will achieve it later without special rules. It also serves as an equalizer: there will be foreign cities slowly getting there. Though the latter is just speculation; I haven't seen a foreign one, but my games didn't reach 1950 (I quit when victory is assured).
no form of wonder-hoarding should contribute to legendary cities as per my argument. therefore, culture from wonders should NOT count toward legendary city growth.
Wonders are what make great cities unique, I think it would feel kinda unrewarding not to have them count. I remember people complaining when the game came out about wonders just generating a single culture point. There IS a system to counter the wonder madness, albeit a gentle one and turned off by default. I called it "REDUCE_WONDER_HOGGING" and, among others, it adds a -3%
modifier to all wonders for building future ones in that city. In my last game my capital was at -24% at turn 175! (That's deserved for having a too good starting location.)
Madrid has surpassed Tenochtitlan!
That would be pretty cool, and certainly doable. It would require (dynamic) data structures to keep track of all cities' progress on various fronts, whereas now the culture level is a single (available) value I consult. I took the easy way and I think for now that's how it will stay
I have tried the same today by the way: get three legendary cities. My game went smoothly (some luck no doubt) and barely missed a wonder I aimed for. After my third city became legendary I had only 6 turns left to go to complete the final branch. At this point I was about 1/3 into the modern age, so there were still cultural goodies to come. As all went perfect for me, this means it doesn't need to in order to have a shot at the cultural victory (but it does require dedication!); I'm very happy with how it turned out!