I enjoy both aspects of hunting and shooting. I'm a gun guy I spend all year pretty much working with a rifle to get it ready to hunt. There are hunting opportunities that will fill your desire to pull the trigger and big game just isn't it for you.
You should take up bird hunting like pheasant, quail, dove, duck, or goose. You'll have good and bad days hunting, but the good days will let you shoot a bunch, not 100+ rounds but you'll get to shoot. If you head down to Argentina for a dove hunt you might get the opportunity to shoot 1K rounds a day!
Another good thing for you to do is take up varmint shooting like prairie dogs. I don't call it hunting because it really is just glorified target practice. It isn't like the game is elusive, you drive out to a town set up a bench, shooting mat, or card table and proceed to see how many targets of opportunity you can knock down. In a big town on a good day 300-500 rounds of can be shot pretty easily, it is very common to have several rifles of the same chamber so you don't really ever have to stop shooting, just swap out rifles as the barrels get hot.
Hunting coyotes can be quite thrilling and satisfying for the shooter that wants to hunt as well. Things sometimes happen fast, especially when you call in three or four dogs. That is where a semi-auto rifle or shotgun comes in very handy. Taking multiple yotes in a day isn't uncommon, and you might get other opportunities such as bob cat.