Does the NRA count as being a member of a “club”?
Sorry - I don't know.
You can contact CMP and they will will help you find a club and get qualified.
Go to this page: http://www.thecmp.org/Clubs.htm
It provides more info, a way to contact CMP by phone or eMail and has a way you can search for affiliated clubs in your area.
One of the easiest ways to qualify is as a veteran
If you are a vet or have a friend /relative who is a vet and belongs to the American Legion, VFW, Marine Corps League, etc. all it takes is filling out a few forms.
PS - I saw boxes of the CMP 30-06 ammo for sale at a gun show last month - asking price was $200 to $250.