Not sure it's true that AI cheats (how?)
I don't think they "cheat." I think a lot of players think they cheat because they, intelligently (a rarity for the AI), run projects to beat the player to a prophet, and the player isn't checking the progress screen often enough. They just figure, "I'm 12 points ahead of the second-placed guy and making 3 points per turn vs. their 1, so I got this in the bag." Then the AI run 2 projects in 6 turns due to deity AI production bonuses, which is not cheating, and the player is dumbfounded.
I did have one particular game where I am confused in how I was beaten and very suspect of the incident. Unfortunately, I wiped my HoF and saved finished files when NFP came out and this was before that, so I don't have a save or any proof. To paint the picture a little, I was playing as a civ (THE civ) whose abilities grant the option for first religion (Peter). I guess you could say I was the one cheating because I wanted to try out a particular strategy and set the map setting to cold and re-rolled until I started in a fat tundra strip which could have not just the capital but 6 or 7 cities whose territory was predominantly tundra. (the experiment was to gauge just how effective faith was in supplementing a tourism victory - spoiler - very effective.) The problem was the lack of food in tundra meant that cities couldn't grow past 4 or 5 pop and getting the extra faith from working more tiles was the centerpiece to the strategy, so Feed the World was necessary. So I bee-lined a religion to the Nth degree, Astronomy first tech and luckily was boosted (Matt's Tilapia wonder, an underrated one.) Once I got to size 3, I opted for halting growth to work the highest production tiles to get the lavra asap, then ran two projects. I'm checking the progress screen every turn and no one else even has a HS yet, so it's just a matter of beating Stonehenge. I cringed when I heard the wonder notification, but it was just someone making Great Bath. 1 turn away and still no one is even generating a single prophet point. I get my religion but the era score was wrong. I checked the great people screen, still no one was generating any prophet points. I checked the previously recruited screen and sure enough, an unmet player got a great prophet. Luckily enough, they chose Choral Music, so I went ahead and got my belief and had a great game. Oddly enough, about 15 turns later Stonehenge was built. I loaded an auto save on the turn that they got the first great prophet, and it was the same turn that Great Bath went. I later find that the player that made the wonder was not the same player who got the first great prophet. So is there some Deity-specific bonus where rarely (this hasn't happened since, although I did have a similar experience when I was racing for GS Zheng Heng and someone got him first, who wasn't generating any GS points) when one Deity AI gets a great person when another Deity AI builds a wonder? Maybe if they were racing for that wonder and lost to another Deity AI they are compensated? Because if they didn't build Stonehenge (it popped later) and they weren't generating any prophet points meaning they didn't have the district to run the project, and after later meeting them there was no way they accumulated the gold to buy them and didn't have a faith generating pantheon, how else could they have gotten the great person?
As for the OP, the reason you can't adjust the number of religions is so that there is competition over getting a religion, and there will be winners and losers, though often the losers didn't want or try for one anyways. Your option of lowering the number of players circumvents this, which I know wasn't your intention but is a side effect. I guess it would make sense if number of religions was based on number of civs rather than make size, but it's probably too late that anyone at FX would do anything about it.
As for alternates, I never liked the Great Prophet format - it's strange that every other great person you get more of if you have the most points per turn in that category, which gives you benefits in that category and forms strategy. But with prophets, the first one you get gives you a prophet and then while your faith accumulation is still pumping, your great prophet point accumulation is discarded? Why not do it like they did in previous games where the first player to X faith (or great prophet points) get to found a religion by being granted a saint or caliph or whatever, a "founder" unit, and then great prophets function like the other great people, where this great prophet makes your theater square adjacency provide faith as well and that great prophet makes your shrines produce gold equal to their faith output? I guess they may be weary of offending by tying this bonus to a religious historical figure like Laozi or Jesus, so just make up names. Joe Bob Briggs founded this religion and Clint Howard founded that one.