National MM9224.

Almost certainly not. 9224 is the date code.

AFAICT, the date code of Q15 is 9920 and for the relays it is 9807.
Would it make sense for a manufacturer to use old mask ROMmed stock in
a new design?

Yes. Where I work, we have "masked" [actually they are OTP, but they
are factory-programmed and sold as "masked"] COP micros dating back at
least five years. We'll still be making those products five or six
years from now, and those chips were last time buy two years ago. Less
expense and trouble to do a last time buy for the product's expected
lifespan than to port everything to a new micro.