I can add another variant spelling: Fults. My great-aunt and I have been tracing our family Fults roots, and we found that within two or three generations, the name changes from Fults to Fulks. The family rumor (still trying to prove) is that the name was changed by railroad company where an ancestor was employed.
I also trace my Fults/Fulks/Fowlkes line back to Gabriel. I only recently made this link to him, so I have not yet done much searching in the Denbighshire area yet. I'd be interested in communicating with others who are also doing research on him. My e-mail is email@example.com