Madscientist covered just about everything, plus plenty that I didnt already know.
To me, it seems like you are picking the wrong civ and map type. Speaking from being able to comfortably settle 12 cities by 1 AD on monarch, and 9-12 based on how many commerce resources I have on Immortal, the key to succesfully playing a REX strategy is by using one of the following leaders, in my prefered order from strongest to weakest:
Darius - FIN / ORG is the best combination for cutting down expansion costs early on, plus a great early rush UU and +2 UB which basically means you have the main EXP trait bonus as well. Also consider playing as Darius of Holy Rome for the Rathaus. Darius is ideal for non coastal maps.
Willem van Orange - FIN / CRE allows for great early REXing with cottages, cheap libraries, and free border pops allow you to settle any good city site with resources two tiles away. UB is very good for Archipelago maps, and also build the GLH and keep all your cities coastal. No need unrestricted leaders unless you are not playing an Archipelago map and want to use FIN / CRE.
Hannibal - FIN / CHM another archipelago map civ like Willem, you want to use GLH rexing here too. You dont get cheaper buildings or free culture, but you do get extra
which means larger cities and more tiles worked - start your cities producing Granaries as usual, and then whip monuments for 2 pop if possible for lots of spillover, or build it for one turn then whip for one pop. Your cities will be able to work 2 extra tiles. All this and we havnt even looked at the UB which adds yet another trade route to your cities! You want to pick up compass ASAP and you can use it to trade for Alphabet / Mathematics / Calender / CoL and currency while rescuing your economy with Cothons. This is a very powerful tactic, with GLH and currency you will have 5 trade routes per city. Unrestricted option with hannibal is not worth it, only use him on archipelago maps.
Pacal II - FIN / EXP as the civilopedia says, wealthy, healthy and happy make Pacal a great choice. You get bonus
with ball courts, get your workers out faster, extra health per city, and faster Granaries and Harbors making him ideal for just about any map type. For unrestricted options try Pacal II of Inca or Carthage to greatly boost the advantage of EXP - Pick Inca for inland games for border popping with Granaries, or Carthage for Archipelago maps with GLH and cothons.
Elizabeth - FIN / PHI makes a great choice for inland maps and specialist economy. Try to set up a Great Merchant farm possibly using the GLH, or even just caste + merchants, and settle as many great merchants inside your best
city as possible to power up your economy. The bonus of doing this is combining Philo with the Stock Exchange - lots of settled merchants plus an extra 15% Gold can create a very powerful mid game economy. You can also try playing as Korea to take advantage of PHI + Seowon, but the Stock Exchange is better.
Other ones I havnt tried yet are Hauyna Caupac of Mali, and Victoria for FIN / IMP because Elizabeth is a lot lot better anyway.
Wonder spam is not used in REXing, except for the GLH and if you marble you can try for Parthenon, Great Library, Mausoleum and Taj, but you cant be wasting your time on other ancient wonders. Collosus can be added to your GLH city for more Great Merchant points, but I never manage to build it on Immortal, but up to monarch it is very possible and gives you more Great Merchants to settle. The more GMs you settle the better, and the more cities you can afford to build.