Similar to the Pilgrimage of the Seven Graces, TR has currently six pilgrimages, with plenty of room to expand from there. Pilgrimages are primarily used both in vanilla MW and in TR to give players an excuse to wander through beautifully crafted exteriors they otherwise wouldn't have a reason to. While this is an admirable goal in itself, it also helps if the trials are a bit more involved than "bring x to shrine get buff quest complete". The Shrine of Courtesy (drown yourself and give a silver longsword to a dremora) shows these tasks are meant for only the most ardent of believers; there's a reason you're sent to these before they trust you with anything else! The last temple quests are the Pilgrimages of the Four Corners, but those are more Daedra involved. I could easily see some of these being converted to work with that as well. With that, here are some suggestions for shrines:

• Gouge your hand with a ritual dagger and let the blood run onto a shrine or stone.
• Another shrine could ask the player to remove all clothing and armor and walk a path to the actual shrine location. One potential way of scripting this would be generating invisible armor pieces for every slot and force equipping it, then failing the quest if pieces are removed
• Opposite to that, a shrine where you are forced to walk a 'Path of Blind Faith' where you put on a helmet that completely blinds you and you have to find your (short, let's not be masochistic) way to the shrine; the quest would fail if the helmet is removed
• A shrine of pacifism where a combatant (priest / dremora / anything, really) punches you for a while until they give up and you pass the test
• A priest tasks you with carrying a heavy weight / boulder / bag of grain up a steep slope. Somewhat done in Bloodstone

Feel free to use any of them or none of them, or even convert some existing shrines to make them more interesting