(I'm assuming that Kate can reliably predict Joe. I didn't initially realize your objection might have more to do with that than the structure of the problem.)

Yes, that is where my objection lies.

ETA: And the fact that in Newcomb's problem, there is no opportunity after learning about the problem to precommit, the predictions of your behavior have already been made. So allowing precommitment in the marriage proposal problem sidesteps the problem that would be Newcomb like if Kate were a highly accurate predictor.