Question

I have a few questions around the 3-move. I know it's NOT an unknotting move (but who needs knots with 20+ crossings anyway :-) by the recent proof of Przytycki.
1. In another paper about the third skein module, he conjectures about a knot polynomial based on a cubic skein equation. Is this polynomial still conjectural (at last so I understood the paper)? (I'm not up-to-date with the literature, naturally.)
1a) Regardless whether yes or no, is this polynomial "meant" for directed links?
2. Instead of 3-move, consider the skein equation
$S^2+a1*S^1+a2*S^0+a3*S^{-1}+a0*H=0$
(where S is the S matrix and H the Temperley-Lieb generator/the 0 tangle). This is more or less equivalent to the 3-move (e.g. I always "knew" the Borromean double would spell trouble, which also was the timewise first counterexample for Montesino-Nakanishi). I say "more or less" because if you eliminate H you are already in the fourth skein module. Also this is for undirected links only. But I only want to know if the unknotting power is the same, i.e. deleting clasps unknots exactly the same knots as the 3-move.