Is there a way to make sure my UE always runs last in the list of a scripted record? I know how to manually move it to the bottom of the scripted records page but is there a way to make sure it's always at the bottom?

no, as you write new scripts on that record you will have to move it manually

could you perhaps move that logic to a scheduled script or something?

The UE kicks off a scheduled script but the problem is I get record changed errors from the other UE scripts, even in the scheduled script after loading the record again.

that problem gets much worse if there are workflows in play