Yea the trickster god will only work if you can ensure you only get credit for each tile one time (or maybe each improvement?). Otherwise you can just build a fort, get the yields, then start a farm/village to remove the fort, then replace the fort.
If your average improvement takes 5 turns, you don't build roads, and you never lose turns walking, it would be 2 faith and 1 science per worker. In my current game I was pretty aggressive with workers (progress and I built a worker before settler), I have 5, so that's optimistically 10 faith and 5 science per turn, which is too low on faith to get a religion, and the side-benefits are low too.
Double the numbers and it looks decent, but only with those really optimistic assumptions. I think you probably need triple the current rate, but even then we need to make sure there are no gimmicks attached.
The idea was that you could try to make an enhancer which really bites and holds. I get that the best defense is a good offense with normal play, but there are some exceptions and corner cases which make resistance more useful than pressure:
widely spaced city placements, like on archipelago maps
expansions on other continents that you want to keep as your own religion
Enhancers need to be able to compete with zealotry, or 2 great people points of all types in your holy city. I don't think a corner case where I get to avoid purchasing a handful of inquisitors is competitive with the other enhancers. This idea could be part of a belief, but not on its own.
For the sweat lodge to be good it needs another effect. Currently we have buildings that boost culture, science, food, and gold. One for WLTKD, one for military strength, pagodas (they are their own thing), and finally Stupas, which are either for tourism or giving yourself a handicap because they game is too easy, I'm currently not sure which is true. They all give happiness or faith in some form.
So it needs an effect won't overlap too much with those. Some themes could be production, border expansion, great person points, or maybe city states?