I am not sure that troops who are granted land should necessarily take longer. For example the Ottoman Timars were used as a fast response low cost force to take on military duty without the need to pay them as a staqnding army. They would be raised quickly, perhaps instantly like levies because they were already trained and equipped and merely needed to be mobilized and thrown into battle.
What I was thinking was that those troops (knights, timarli, other nobles) should be a standing army rather than a quickly recruited force, since they did cost a lot in upkeep during peace too, letting someone have state lands and not asking for tax is a big loss of income. If they were already built they could be mobilized instantly after all, I think the building should represent giving out fiefs or waiting for noble youths to train. Allowing traing of big stacks of nobles fast would be strange as there are only so many availible to mobilize.

Happyness for "temples" is good. At least in protestant sweden the church also had a police role, preasts were helping with bureaucracy and keeping an eye on dissidents, and levy recruitment (at least after 1680, I'm not sure about details). I doubt the monasteries gave the same benefits though, these I think were more for learning and for locking landless nobles away (locking jobless nobles away might have helped reduce rebellions though).
Yes monastery orders could be a good idea. Sufi groups/orders are hte same sort of thingin the muslim world arn't they?