Civ 5 Mayan Civilization

The best time I've ever had playing Civ 5 was with the Maya. Two things I observed:
1. The Piety tree seems to be designed for them. The extra faith and especially quicker building time for shrines works great with the Pyramid. Plus you can do awesome things with the right Reformation belief (see below).
2. Using the science boost from the pyramids to rush Theology is totally awesome.
In my game, I researched only the technologies necessary to get to Theology to make the most of the Mayans screwy research priorities. Then I started building the Hagia Sophia immediately so I could get a great Prophet. Although it took many turns, it turned out to be worth it because my pantheon belief was Desert Folklore and I was in an area full of flood plains, so I ended up with two great prophets coming out at about the same time. This allowed me to found and enhance a religion long before the AIs. When the Long Count kicked in, the first Great Person I chose was the Engineer, which I used to rush production of the Mosque of Djenne so that my missionaries would be able to spread religion three times. After this, I started building Borobudur, although this ended up running into issues.
My second Long Count Great Person was another prophet which I used for the improvement and I think I spent more faith on another prophet, giving me two improvements in addition to the faith from desert tiles and the pyramids. I also had my first follower belief, Divine Inspiration, which gave me +4 faith for my two Wonders. For my enhancer belief, I chose Holy Order (missionaries cost 30% less), so I was able to spam out missionaries quickly. Luckily, the desert I occupied was surrounded by land on all sides, so I just sent my missionaries out in all directions. Because I couldn't negotiate Open Borders treaties yet, I chose primarily to use my missionaries on city-states in order to avoid the penalty. Since no other civs had come close to founding a religion yet, my religion started spreading accross the whole Pangaea map pretty quickly. But that was just Part One of the awesome. Because I chose the Piety Tree, I got a reformation belief. I chose Heathen Conversion so that as my missionaries went abroad they were #1 safe from harm and #2 recruiting a massive army. It was still early enough in the game that many barbarian encampments were still operational.
For my founder belief I chose Initiation rights, giving me lump sums of 100 gold every time a city converted, which added up to a fortune this early in the game. I used the gold to buy catapults (which I had made my next research priority after completing theology). My second follower belief was holy warriors, so I was able to buy some catapults with faith. For the most part, however, I just kept spamming missionaries.

That's when my plan hit a snag. I had converted so many barbarians from all across the map that bringing them together with my catapults to launch a coordinated assault proved difficult. As I was trying to gather my army from near and far, my missionaries kept spreading the religion and converting barbarians. The problem was that my army was too huge for my population, which was still pretty small. I had never encountered this problem before in civilization where the population cannot support the military. My capital city stopped being able to produce right when I had almost completed Borobudur. I needed to finish that wonder so that I could start building more catapults to take down cities. At this point everything began to fall apart and my game became a disaster all because my plan had been too successful.

Is there any way to make this approach more sustainable? Or is it perhaps just too ambitious?

My experience taught me that despite appearances the Maya are a force to be reckoned with. It was also a lot of fun. :)

I think you just have to delete some of your newly converted units, even if they are not in your territory.

I'm going to try this strat with raging barbs, its going to be nuts.

Maya

Social policy: 1, Tradition for the border expansion and +3 culture, and to be able to access +15% wonder speed if you get into wonder races with another science civ. 2. Honor for free culture pounding barbarians with Atlatlists 3. Liberty for +1 culture per city, then 4. the free worker, then 5. each city costing 33% less culture. Then send settlers out and sit them where you want, getting 6. Piety so your pyramids cost half as much in each new city.

Or focus: Piety (half cost Pyramids), Liberty, production bonus and then free settler, if you don't have enough barbarians around to make use of honor or aren't cramped in by neighbours enough to worry about border expansion speed. You will however pay for workers, or kidnap them from city states.

Science: Straight to Theology but add Bronze Working if you have jungle as you need those plantations. Or Sailing if you have pearls and crab around instead, and Optics if you have to embark to get to the good places safely. At most two techs that are not on direct track to theology. You should have theology before 1000BC in every game if you do it right. Choose other techs only if they speed you up on the way to Theology. You will be very happy in late game when you have taken all 7 GP types and cycle around to get another GS just when you need oh ah Refrigeration.

Expansion: Quick 4 cities, fast NC with MotG and Pyramids that's +18 (4 per city and +2 more from NCs +50%) than any other comparable civ. You'll take off like a rocket, pun intended.

UB: Always build it first, then libraries, then universities, unless you need happiness buildings.

UA: 1, Great Scientist first, build academy near your fastest growing city by a Mountain in a jungle, if possible. 2. Great Prophet, make sure you enhance your religion first and spread it very fast.

Religion: Tithe+Feed the World+Pagodas+Religious Texts.grows well but Messenger of the Gods gives great early science and rewards big cities. Also the 10% growth bonus and 15% at peace growth bonus are really hard to pass up, as they expand your specialists, great people and borders and production also. If you do Piety you can eventually get the Reformation belief, Heathen Conversion is very powerful if you get it early enough.

I know this is late to the game, but the Mayans are truly OP.

Go straight for theology, get a great engineer engineer early, focus on maxing your capital. You will win the race to Frigates or Muskets, your capital will be able to leave build a new unit every other turn.

Simply take your 2nd city by force instead of building it.

In a game which I built the great library, I had a few frigates by 300AD. Easy to crush all with that tech advantage.