Check
http://www.odcmp.com/Clubs/List.htm for a list of CMP affiliated clubs. USPSA and Garand Collectors Association are both affiliated.
I believe that they are very liberal as to what qualifies as a "match." This is from the application form:
Have participated in a marksmanship activity where
at least 50 rounds of range firing were completed.
You must provide a copy of a results bulletin from a
competition or clinic completed with-in the last five
years or other proof you fired at least 50 rounds or participated
in other CMP approved marksmanship activities.
Providing proof of military or law enforcement service
or proof of Distinguished, Instructor or Coach status
will satisfy this requirement. This requirement is waived if
your proof of age shows you to be at least 60 years of
age. Proof of marksmanship not required for purchase of
drill rifles.
It looks to me like shooting any competition, even IDPA type stuff, qualifies for the shooting requirement. You still have to belong to an affiliated club, but I do not believe that there is any linkage there.