So after playing a few more games I am actually at a point where I am willing to drop the Inca and make the Maya my main CIV (for reference: King difficulty, 4 cities total).
Weirdly enough I actually feel that they are pretty consistent when it comes to terrain. You need to spawn in a place where you can find at least 3 decent city spots around the capital, but as long as it is not ocean or a giant desert / mountain cluster the Mayan cities seem to flourish pretty consistently throughout the game. However, that means they are quite map dependent, and you'll probably want to stick to anything with a lot of continuous landmass (Pangae, Seven Seas, Inland Sea, etc.).
Their flatland bias means that you tend to have at least 1-2 solid tiles for the initial farms to kickstart the city. You also tend to be near rivers with at least some floodplains, so you can set up Aqueduct + Dam combos to provide solid early to mid game production, and later down the line you can use the outer forest & hill tiles to get enough hammers to sustain a solid (at least for my playstyle) production ratio. Thanks to the farm housing you will never really have to worry about the city size max past the early game, and a neighborhoods are only necessary to get the Food Market or Shopping Mall.
I think a key to their success is to get a builder (and settlers, duh...) as early as possible. The extra gold from those early farms & plantations snowballs into another builder, which then gives even more gold, and so on. The amenity bonus from settling next to luxuries will allow you to get a slightly larger than normal city during the early game, which can compensate for their slower start & the flatland terrain inefficiency (the Colosseum also seems like a fantastic wonder in that regard). I noticed that I was doing significantly better than the Inca whenever I got to pick the extra Settler or Builder pantheon (my new best science victory timer was 300 turns, while I usually take about 350 with the Inca).
I have started to focus really hard on early game tile improvement with them, to the point where I even push back my archers a bit (albeit keeping a bot of gold in reserve, just in case an AI decides to beeline for me). It is dangerous, given that the barbs can be really aggressive, but their UU & extra combat bonus around the capital are pretty good at keeping early aggression in check. I am still putting down Observatories early on, but I tend to delay the library to squeeze in another builder first if it is adjecent to a plantation.
One thing I'll say is: Don't put your early farms on floodplains. It is simply not worth the risk, even if there is an extra yield on the tile. Losing them to a flood will not just ruin your yields but also cripple your housing.
But, yeah, overall the Maya have really grown on me. I don't think they are a particularly great CIV for competetive play, but they seem very much ideal for my tall, peaceful builder playstyle on a relaxed difficulty.