I'm going to use the suggested brand of thinset, but since as an old automotive guy I'm just not comfortable with so much "free floating" filler, I've acquired some of this stuff:
I'm going to cut it into strips sized to fit the problem area, and then apply a coat of thinset, then a fiberglass strip, then more thinset to build to the correct depth. That's gonna be the toughest part - determining how thick is thick enough without going too far.
I'm goint to try to err to the side of "less is better" and then make it up with the actual adhesive layer to the tiles.
Plenty of time to dry before applying the tile layer of course. Does this make sense?