Great Temple does not help religion In the holy city... it only helps religion coming From the holy city. (and it helps whatever religion is dominant, if your holy city is converted it will spread that other religion at +100%)
Hopefully Browd will jump in and clarify this, but I don't think the above is correct.
As I understand the Mechanics, a Holy City always generates 9 pressure for its own faith, even if it has been converted.
Two nearby cities of the same foreign faith would be 12 pressure, so that alone might be enough to prevent the original religion from reasserting itself. In this example, the Holy City following a foreign religion would also exert 6 pressure on each of the two neighbors. So I think a converted Holy City is an example of a city generating extra religious pressure, 15 total, whereas a Holy City is normally only 9.
Grand Temple generates extra faith, but not extra religious pressure. It generates that faith regardless of the religion of the city.
If you have 5 cities of the invading religion in range, your Holy City will Not recover on its own, you will need a Prophet or Underground Sect to recover your religion then.
Any GPr you faith purchase will be of your religion. So even if your Holy City would never recover on its own, recovering your religion in your Holy City and three nearby cities is trivially easy.
also this effect lasts even if the Grand Temple is destroyed, I've had captured enemy Holy cities sending out +100% religious pressure
Right, because significant religious pressure comes from every Holy City. Grand Temple is extra faith, not extra pressure.
The problem has little to do with the ability to spread to your own cities or maintaining religious pressure. The problem is having 2-3 Great Prophets inside your borders per civilization that has a religion (so maybe 6 or more prophets in your border at a time.)
Yes, that is a problem, but only a small problem. You would not want to be trying to convert your own cities back while that is going own. Fortunately, the GPr spam will not go on indefinitely. But you could prolong this unpleasant phase of the game...
Having an inquisitor in a city prevents the prophet from flipping it, so having 1 inquisitor in every city would prevent any of them from being flipped... [but] prophets are lingering in my terrain before 1 inquisitor/city is an option.
I am still not seeing the problem! Let the AI convert your cities, buying foreign faith buildings as you can. The GPr will be burning themselves out, especially if two civs are fighting over your cities. Staffing all your cities with inquisitors is actually counterproductive because then the GPr just mill around your territory and might never go away. On the other hand, if the foreign GPr keep converting the same city over and over, and that city already has the foreign faith buildings while others do not, then investing in a inquisitor might be helpful to spread out the foreign interest to be of better utility to the player.
And I know that having a bunch of prophets in your borders is a reason to consider DoW and capturing Holy Sites, but on Deity there are a lot of considerations regarding when to declare war including feasibility of defense, perceived ability to advance and take cities, and diplomatic impacts.
Even on Deity I think a single GPr that can be planted is worth DOWing over (but not breaking a DoF over). The problem is that, until you capture it, you cannot tell a one-use GPr from a virgin one.