I think you need to accept that some things in language just are.
I am parked over there.
Of course, the speaker is not parked, passive; s/he parked her/his car, and the car has been parked - and therefore is parked. However, I am parked is used and understood by native speakers.
Similarly, I am paid up/off is used, and understood, to mean that I have paid all my debts, all my debts are paid. Paid up/off can perhaps be considered to be an adjectival phrase meaning "in a situation in which no more payments have to be made".