More bits of info you may find useful:
1) The "Authorization for Release of Medical Information" is not required, and so does not need to be either signed or notarized.
2) If you're applying as an honorably discharged veteran, you can use a special code to get fingerprinted through the Cogent ID website. The ORI is NM920272Z. You can find it through the search feature by searching "DPS CCW LAW ENF APP". That will save you a few bucks. Wish I'd known this, could've saved $44. Oh well.
3) If you live in or near Albuquerque, you should make time to go apply in person at the NM CHL SID office (6301 Indian School Rd NE #310, Albuquerque, NM 87110). They will need to look at your original birth certificate, but they will return it to you right away. That sure beats mailing it in, and hoping it doesn't get lost when they mail it back.
They are currently taking about 30 days to get new CHL's mailed out.