How would you feel of switching the founder and enhancer beliefs though?
I think I wouldn't like it. When I found a religion, I should then start benefiting from that religion. Postponing actually getting any benefits from religious founding until the religion is enhanced (which might be medieval era) is too late IMO.
I think it would be frustarting to have to be 2 great prophets in before I start getting spread benefits, and I think it would be hard to balance many of the expansion boosters if they are available as soon as the religion is founded, as there is a lot of snowballing potential from an early religion spread.
To go with your analogy, I'm not sure the enhancer beliefs should be modeling the spread of Christianity to Rome, I think it would be more modelling the spread to the British isles, to Spain, to Germania, to Russia, and so forth. But that's subjective of course.
*edit*
The other bigger problem is: the founder belief goes only to the founder. But IIRC the enhancer belief can benefit any civ with that religion present. So with your proposal every civ gets benefits from you widely spreading your religion, when those benefits should accrue only to the founder.
(1) So what do we got here then: Tourism, City States, Science, Gold (buildings), War, Great Persons (Reliquary?), Wide Empire/Settling?, World Congress, Culture (buildings)?
I'm not sure that culture really qualifies, culture doesn't get you much by itself. Otherwise generally fine.
however it doesn't solve the (possibility of) a big imbalance (for a designed religion) between faith generation and faith costs which was the idea behind the current distinction.
A fair number of the reformation policies would function as faith sinks, if you wanted that. Science and gold building purchase beliefs, military unit purchase beliefs, a monastery building belief, all let you spend faith to get stuff.
Another idea (probably not feasible): what about a reformation ability which let you spend faith to increase influence with a city state if you shared the same religion?
(2) I still would love to have a generic policy allowing the construction of a building by faith for that effect.
This would also be fine with me. Take out the golden age stuff, which has no particular Piety synergy. I'd love to get rid of all the dud social policies.
But I don't remember whether a Monasticism policy was technically feasible or not. And there could be balance problems with Sacred Sites if you can get 3 religious buildings per city *and* sacred sites.
I'd also like to strip out the missionary/inquisitor changes, I don't see what was wrong with the vanilla values. 300 faith missionaries seem too expensive in the early game, and too cheap later on.