Incorrect 1099

Client received a 1099-MISC for rents. It should have been 1099-NEC for services. Payer is not responding to requests for correct 1099s.

I'm going to put on Schedule C where it belongs. However, should I also put it on schedule E and zero out with corresponding expense? I want to minimize the possibility of client getting a notice to which I'll need to respond.

That's what I'd do.

Report as gross rents on the Sch E. Back it out with other expense "Reported on Schedule C"

Don't bother pinging the issuer if this is a one-off 1099. You're wasting your time.