There is a variation that is well suited for your idea. That is, NRA sporting rifle.
The basic rules are as follows:
Standing eight shots slow fire in eight minutes.
Two strings of rapid fire sitting or kneeling with four shots each string. You start with the rifle loaded at the beginning of each string. The time is 30 seconds for the string. The usual commands are: "Ready on the right, ready on the left, all ready on the firing line. Commence Fire"
Prone rapid is essentially the same as above.
Prone slow fire finishes (or starts the match as our club does it backwards).
It is a 32 shot match for record with eight shots in each position.
Sighting shots (usually five) is given before the shots for record. It is the reason our club starts in prone, as that is how most shooters want to do the sighing shots. It avoids the extra time needed to change set-ups for position.
Eight shots on that target are normally easy to score.
Our club also has a 50 yard version on a 1/2 sized SR-1 for rimfire and air-rifle. I've scored at or above 310 a couple of times with my air rifle (scoped). I often score near or slightly above 300 with centerfire (irons).
In sporting rifle, scoped rifles are allowed, as the game is intended to introduce those with deer rifles to the highpower game.
Our local club will be starting our matches later this month. We shoot one match in May, two in June, two in July, two in August, and one in September.
Count me in for the postal match.
ETA: The complete Sporting Rifle rules are available on the NRA website.