Ok I'll bet the hostage is either Androssi, Rachel, or both (covering my bases).
I've thought for many years now (...wow!) that there will turn out to be a part of (secret) tower/princess lore and/or Arlene's prophecy that will make Baam getting paired off with a princess into an essential part of fulfilling the prophecy (and the tower's destiny).
Seeing Traumerei offering Baam one of the twins has me revisiting that idea and, frankly, it still seems plausible (...with me suspecting the narrative reason they're twins is to depersonalize-and-diffuse the eventual rejection and/or to let one die).
If nothing else, hearing talk of family heads butting heads over Baam makes me wonder if Maschenny really is going to try and hook Baam up with Maria. Didn't see that before but could see if it if we see ToG turn into "bachelor in the tower".