Huh, wonder if the phantom weapons' 'large' is different from the usual 'large' in weapon skills. Or if it's a rush/barrage thing. Cause I'm really interested in the hammer's extra-large now. Not that regular weapon skills ever got XL, I think?

Regarding Tower Quest:
Tower quest events ask for single element teams, not mixed.
The first tower quest event (Phlox) is fire, and 1/3 of the missions ask for water only.
The second tower quest event (Nero) is water, and 1/3 of the missions ask for thunder only.

The 'use only X element kamihime' missions add up to ~2550 medals out of the total 10,000. (not counting the tens of medals you get for clearing in X range of turns)