Two ways to go with "aris," neither perfect: there's the Greek "aristos," as in aristocrat, which means "the best." (Aristocracy is government by the best.) Going that road would make Polyaris a sort of Holy Ghost stand-in, which I think its a bit much (but maybe not, in this already too simplistic story). Then there is "arris," of which the single r version is a variant; it is the sharp edge formed by the contact of two plane or curved surfaces, i.e. the edges of a prism. In that case, Polyaris is simply a witty name for a glossy multicolored parrot. (Poly as in "wants a cracker.")
"Kul" in Greek is the Latin "cyl" as in cylinder, and it means (or derives from) "to roll." I can't make much of that, myself.
It's hard for me to take this story seriously when I keep humming the title to "California Dreamin'!"
-alga-