Still doesn't work
Shame, but it was worth a try.
You can't reform a religion without religious buildings, and that's my initial question, how long would it take in game to wait for the max prosperity in the holy provinces, wait for the event that adds a building slot, build a temple in each province and reform your religion and is it only possible ?
About 200 years of serious focus on prosperity should do it. (Get and keep 3 holy sites at prosperity 3; move your capital to one of them and set crown focus; feast/fair/raid/etc as often as possible until the +slot event triggers; move to the next.)
For context, I can normally manage to get 1-2 extra slots per county in my capital duchy by about 300 years after game start, including the inevitable reset-to-zero from the black death. I expect that defending the prosperity of 3 widely-spaced counties will probably be a lot harder than defending a single duchy, but you only need one slot in each county. Hence, about 200 years.
For this approach, I suggest you either turn off the black death or push it far into the future. (It takes multiple decades to go from depopulation 3 to prosperity 3.)
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Since you only need one slot in each holy site, there is another alternative: the free slot from great works. Build a great work in each holy site to at least tier 2; remain at peace; build an improvement; continue remaining at peace; a different +slot event should trigger about half a year later. (And this extra slot is free.)
This approach has the advantage of being completely independent of RNG - but you will need to amass a LOT of wealth, and building great works can take quite a long time. But I guess you could cheese it with 3 gardens if you were trying to speedrun (<20 years after you conquer all sites, assuming you have unlimited wealth).
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However, probably the quickest (and also RNG-independent) approach is: start as nomad (or become nomad via
inheritance conflict or other methods); conquer the 3 holy sites; pillage the existing holdings; build a temple.
If you don't like or can't do the nomad option,
you can also do this as tribal as long as the holy sites have castles in them. (Tribes cannot pillage tribal holdings, but they can pillage castles/temples/cities.) Bön is probably the best for this, as most/all of their holy sites are feudal at all start dates. (Ditto Hellenic and Aztec, but they are rather niche.) Germanic is next best, as 2 are feudal at all start dates, so you only need to wait for the AI to upgrade one. Then maaaaaybe Slavic. Everything else is likely to remain tribal for a loooong time, so it's probably not suitable.