Here is what I do:
Once I obtain her highest possible obidience rank, I go with her for around 30 minutes and then tell her to stop following me. Then, without moving anywhere, I immediatly tell her to follow me again. Rinse and repeat until you are at the shrine.
If you are too soon there (which I usually am if I take one of the girls that live farther away) note that you can unfollow them, make them follow, wait one time (regardless for how long), unfollow, follow, wait etc.
(I *think* the game checks how much follow-time you have left everytime you either try to walk somewhere or try to wait, thus unfollowing them and then follow again before doing anything resets the timer..)
Since there is no real reason to sleep in this game use the night to get people where you want them, makes the sundays *much* easier