This seems fine, there isn't anything especially threatening here so I don't think there are really and bad choices. I see three options.
1: deal with the naga, either take the offer or threaten them, this is probably the fastest option and if we go with that I prefer just taking the offer as it doesn't seem to disadvantage us and it is basically certain to work.
2: just pick a door, we have 4 to pick from but we probably can't use the giant one. I don't think we know of anywhere we can't go and someone will probably tell us if we aren't allowed somewhere, we know about "the bath, the library, treasury, The Desert Mother's throne room, dungeons and birthing chamber", at a guess the big door is the throne room, the fancy door is the treasury and the simple one is the library or general rooms. I like the simple sandstone one as overly fancy isn't where you put hospitals (also that might be the treasures Hess mentioned and we aren't looting) and you also don't take people further than required.
3: just ask Hess, she probably has a good idea of where to check, although this obviously takes more time.
My vote is for going through the sandstone door.
If one of them does decide to attack us . . . we fight back obviously, if nothing else it would make threatening the other one easy (or if we lose we can probably get what we need anyway).