I get a consistent bug with prayer tents in that if you research one of the unenhanced, uninfluenced upgrades, that same enhanced, influence-version upgrade is grayed out and unavailable for research for the rest of the game. This effectively locks you out from the enhanced version upgrade if you choose the basic upgrade first. This does not work like, say, the ger where you can complete all of the basic economy research first and later go back and complete the enhanced upgrades with a ger under influence of an ovoo/prayer tent once you have the stone.