Although this may well not be of concern to the OP, jkhirsch, it would be a top concern for me: was a title search accomplished (AOPA does a fabulous job!) prior to this purchase?
At the risk of becoming tedious, the "odd" (to anyone else?) condition of the "erstwhile" dataplate and the (as of today) lack of an updated registration status would make me very edgy when considered individually, to say nothing of their combined impact.
I would suspend all consideration of bringing the machine into compliance until I was certain the A/C was actually mine. I would not want to spend any more resources (mental, legal, or financial) until I could ascertain that such resources were, in fact, being directed in the interest of my property.
Jim