Having vanquished all three demons, I have been going round and round inside the royal tomb for days, but I seem to be missing some secret passage/button.

I have found and opened the central secret passage with the golden statue near its door, but the gate near the entrance of the level below (3rd level, I guess) is closed.

I have visited both sides of level 2, finding two rooms on the west side and four rooms plus a secret 2-room area on the east side, but did not find anything else.
Re-visiting the entire dungeon for each of the 64 combinations of the six switches (at level 2-West) would be too much...

What am I missing?

To get to level 3, you need two keys from level 2 - one is dropped by Princess Theresia and the other one by Princess Rafaela. Check the Royal Burial Chamber maps in this thread to find their locations. Maybe you have missed the key dropped by Theresia and it seems to me you have missed the secret area in the west part of level 2 with Rafaela.

Thanks, Kovi!
In fact I had been standing in front of the secret button many times, but I had to pixel-hunt for it; the "Keen Senses" spell at Initiate level was not enough to detect it.

I guess I already encountered one of the princesses, but she was killed by the monsters as soon as I entered the room (I may have attacked her from afar, mistaking her for a common monster).

...so I learned at last to recognize secret switches without relying on skills or magic and used this newly acquired ability exactly once before finishing the game ;-)
Nice ending(s), by the way.