replace one tile bathroom floor
Yes there is a rapid set thinset, big box stores have it. Fortified thinset that you have is good stuff, I used it in all my install for my bath renovations. 2 days time is not enough time for thinset to get a strong bond, enough to step on but easy to pull, any longer you would have had a tougher time.

The amount of thinset you use is crucial, it has to be placed so the tile is well supported at various heights, but can still be lowered if needed. If there is a high spot in the subfloor, grind it down, I have relived the back of tile in places where needed but that is really chancy. Those areas need a full bed of support under them, so the thickness is critical there, but time well spent.

Get your tile to set below the surface of the other tile uniformly, about an 1/8" to a 1/4" lower with no thinset under it, no rocking, then you can gauge how much thinset you need under it. Except were you may need to grind the back of the tile, floor grade tile can handle a small span with no contact to the setting bed.