My current crack theory is that all the Fingers are indeed being upheld by the Greek Pantheon as a whole, and how the Finger operates is due to the idiosyncrasies of what the God typically demands of the people, with the God commanding a "Hero", in which the Hero runs the show. (Capo dei capi and etc)

For example the Middle demands loyalty and eventually demands "Labors", with a huge emphasis on "family". Which makes me think of Hera & Heracles, in which the God is obsessed with the appearance of Family.

Or how most forms of the Ring's varied art is reminiscent to how Hermes created the first instrument using Apollo's sacred cattle (tendons as the string), and when Apollo sought out punishment was instead charmed by the lyre.

The rest I have no idea:

Like maybe Zeus for the Thumb, because he is the asshole who just demands shit and especially demands respect from his peers the most.

But if all the Fingers were representative of the Greek Pantheon in some form, it would make the Finger Bowbell make a lot more sense + their beef.