Joe, your impression that most NRA and CMP rifle matches are limited to American rifles is incorrect.
Like Jasper said, you can shoot ANY rifle you want at NRA highpower matches. The rifle only has to meet all of these criteria:
1) Be capable of accepting five rounds or more in the magazine
2) Be capable of being quickly reloaded (detachable magazines or stripper/en bloc clips)
3) Have metallic sights
Outside of that, the model of the rifle will determine whether it competes as a service rifle or a match rifle. For it to be considered a service rifle, it has to be an M16A2 or M16A4 clone, an standard M14 clone, or an M1 rifle. Anything else, regardless of country of origin, is a match rifle.
Match and service rifles compete side by side, on the same targets, and through the same course of fire. The only difference may come at match award time.
What you have will work JUST fine.
When it comes to CMP matches, your rifle is classified as an "vintage military rifle" and you can compete in their Garand/Springfield/VMR club matches.