What I said is true. Exemption is not possible.
I did call the MAC (motorist assistance center - in Medford). Actually you don't call them, you call the Registry and open a ticket and they call you back. There's no direct number for them or even an address for them.

They told me explicitly - don't even bother registering the car. You will not pass smog. There's no exemptions any more. They said if you have access to a dealer plate or a repair plate you could drive with that.
Yes, registration is separate. I could register the car and probably get a title (probably). Possibly not even that. They would require me to go to the state police inspection station , show receipts for the donor car and all the parts that went into the car - which I don't have. Also, I would need to buy and install two brand-new not-from-donor catalytic converters.