I think part of the problem is that you have a particular/set way you want to play, which just doesn't seem conducive to Religious Victory.
What difficulty are you playing at?
What governors and promotions have you been investing in?
So it sounds like 6 cities isn't enough to generate the faith you need. Maybe you should be settling a lot more cities? Compact lots of cities and have them reinforce religious pressure. That's one strategy.
Personally, I like giving each of my cities plenty of space (at least their 3 tile radius) but based on the situation you described you might need to compact as many cities together as possible.
Another key factor is what religious beliefs did you choose? Pantheon and Follower beliefs often have a big influence on your faith generation. What Enhancer did you take? If you are really buying that many religious units, then maybe you should choose Holy Order for reduced costs. Did you get any Golden Ages and did you take Exodus of the Evangelists?
Once again, I would recommend hoarding your Apostles. The AI doesn't think about unit conservation. You want gangs of 3-5 Apostles. Then every time an AI sends a missionary or Apostle, you kill it and that is essentially a free religious spread for you without costing you any faith. How many Apostles have you bought throughout the game?
I don't know how you define "warmonger" but you could also go on a pillaging spree (which I did even before GS upped the pillage amounts). Pillaging Holy Sites and Plantations generate free Faith for you. And pillaging holy sites slows down your opponents. I spend a lot of time at war even when I DON'T want any of the AI's crappy cities.
I play at Prince because with the next step up the AI opponents start to get advantages like starting with two Settlers or an additional Warrior or similar things.
I've got all but two of the Governors in play. I _always_ start with the diplomat so I can get suzerainty on City States ASAP. Then comes the guy in the derby hat to improve city productivity. I added Victor, the military governor because my fifth city was "behind enemy lines" and kind of isolated, so defense seemed a priority there. The religious leader was my fifth governor, so his late inclusion probably affected Faith generation, at least to a minor degree.
I was limited in my city building early on because the program dropped three of my 8 AI opponents practically on my first city's doorstep. (All within 12 hexes of my first city.) I had to do "end runs" around them just to get cities five and six. Numbers seven and eight are placed on _really marginal_ locations with very limited numbers of usable tiles.
My pantheon belief was Monument of the Gods because I really, really favor building Wonders for the advantages they give. (Didn't move fast enough to get Stonehenge though. No nearby Stone in my first city.) As much as I wanted to pick 50% discount Apostles and Missionaries, I went with additional charges, additional Housing, immediate new city conversion, and additional envoys for initial City State conversion.
Most of my policies deal with money-generation, so I guess if I switched to faith-generation so I might be able to up faith/turn to @400-500. But even if I did, I would still be looking at @10 turns to buy an Apostle.
I define "warmonger" as being anyone NOT of the "Let's all try to get along peacefully" philosophy. As such, for me, pillaging is a no-no. "Walk softly and carry a big stick" is how I roll. I have Declarations of Friendship with EVERYBODY, and Alliances with five of them. And I'm suzerain over 15 of the 30 City-States (six of those 30 having been absorbed by other civs. In 3100 years of playing, I had ONE war early on when Scotland thought I would be easy pickings. He caved just when I was on the verge of taking his capital. We've been quite friendly since then.
I _do_ engage in religious warfare by having my Apostles fight with their Apostles. I see that as being a battle to "win the hearts and minds" of the city dwellers. (Besides, if I don't attack them, they WILL attack me.) I have found that using Apostles down to having only ONE charge left is a good way to create a religious military force: place a one-charge Apostle next to a city and sooner or later an opposing religious unit will come a-calling. Have several in close proximity to one another allows them to pile onto those opposing units for a quick kill -- which also causes a +250 boost for my Religion in nearby cities and a -250 drop for theirs. That's better than a Conversion charge. Wounded Apostles DO need to run back to one of my Holy Sites to heal. That has become problematic, having to traverse half of a pangaea continent TWICE to get a wounded Apostle back on the front line. (As I extend my railroads across the continent, it's becoming less problematic)
Throughout the game, I have bought about 30, maybe 40 Apostles and only a couple Missionaries. (Missionaries don't fight worth beans. They die waaaayyyy too easily.) Because of the way I use my Apostles, I may very well still have my very first Apostle in play. I've only had about five become martyrs over the millenia..
For Victory Conditions, I disabled, Cultural, Scientific, and Score, with no turn limit. Those conditions are, imho, way too easy to attain. (At least on Prince Difficulty.) I've only got Domination and Religious still active, and I really have no intention of having ANYONE attain a Domination victory. That leaves Religion, and that's why these escalating prices worry me. My endless game may well extend to 5000 AD as no one will be able to keep enough units in play to secure a Religion victory.