I don’t condone layering, and i haven’t tested this myself for the record- But
A guildie of mine asked if anyone had troubles with that exact quest and i mentioned how i sat at the outhouse for 40 minutes without luck so i ended up disbanding it.
He then went on to say he simply swapped layers and he could interact with said outhouse. Not sure if true, but i don’t see why a guildie would lie.
(I can’t decide what my guildies do, other than tell them i don’t condone of layering, although in this situation i don’t see the problem in it, if it works.)