Yes indeed,
I agree that this is serious and interesting. It hovers near the limits of my Math comprehension, so is not easy reading for the Math challenged, but it kept my interest by continually coming back to comprehensible ideas.
I believe you effectively demonstrate that a deformed algebra is necessary, Michele, and it appears that your construction does the job nicely. I will need to re-read for details before I know for sure, but I find the derivation of a non-commutative rule to be a satisfying result.
all the best,
Jonathan