I'm pretty sure I've done everything I'm supposed to, at least according to guides, but it's not possible to interact with the statue base. I did accidentally do the water temple puzzle before hearing the creed from the shade and his wife, does that matter?

Hello, were you able to figure this out?
You should be able to place the totems in their place at the base of the (shattered) statue. Is this what you mean?
If I am not mistaken, the game was either rather finicky about where to click to place a totem or each totem could only be placed in one of the three spots specifically.

Can you share a save file from the spot you're stuck at?

I loaded the save I made after giving up yesterday, and now suddenly I get the blinking interaction cursor and success/failure responses with no issues.