With 10,114 cosets solved in the quarter turn metric, I have shown that 30 or fewer quarter turns suffice for every Rubik's cube position. Every coset was shown to have a bound of 25 or less, except the single coset containing the known distance-26 position.
I also solved every coset exhibiting 4-way, 8-way, and 16-way symmetry, and each of these also were found to have a bound of 25 or less. Thus, if there is an additional distance-26 or greater position, it must have symmetry of only 2, 3, or 6, or no symmetry at all. I believe, based on this, that it is likely that on other distance-26 positions exist.

This effort has required in total, so far, 19 CPU days on a i7 920 and 31 CPU days on a Q6600.

I believe most QTM cosets actually have a worst-case distance of 24 or less; I will be investigating this by solving 25 random QTM cosets fully, if possible.