New Mexico is very gun friendly, no state issues. I don't know exactly where you live, but an NFA trust might be the easiest way to do the transfer. Check with Sandoval or Bernalillo County sheriff and ask if they will do MG transfer aprovals. I don't think either will, and I know the ABQ police chief won't, at least I've been told that.
You might want to check with Ron Peterson's or August Arms to see about the signoff.