> "Cancer" later took on an alternative meaning, "enclosure", because of the way a crab's pincers form a circle.
I am not an expert, but I think this may be backwards. I think the original meaning was circle, from which both the "enclose" meaning and the "crab" meaning (because the pincers form a circle or an enclosure) derive.
wiktionary [1] has the most in-depth etymology I can find, and has for "cancer" (meaning crab) the etymology is: karkros (“enclosure”) (because the pincers of a crab form a circle), from Proto-Indo-European kr-kr- (“circular”), reduplication of Proto-Indo-European *(s)ker- (“to turn, bend”) in the sense of "enclosure", and as such a doublet of carcer. Cognate with curvus.
Anyway, that aside, I felt stupid not having realized the etymology of "cancel," since in Italian (one of my languages) "cancello" means "gate."