Ha, I do all of this already. (My "trinket" is a Yubikey, though I just added a 3D printed MIT Flea tag an enterprising child was handing out at the last Flea.)
I propose that the reason for clockwise ordering is: door locks are on the right, and also most people are right-handed. So looking at the keychain as you would hold it to insert the key into a lock, the first visible key is the first in clockwise order. The others are "stacked" beneath it.