Hard to say if helps, as I've been doing it for longer than I've been shooting seriously, but I don't feel that athleticism or lack thereof is what's holding back my shooting. I'm doing heavy weights for low reps three days a week. A typical workout for me is warming up on big lift (squat, deadlift, power clean) by starting with the bar and adding weight incrementally until I'm at my first work set. I'll do a couple sets of five, typically increasing the weight the first three sets then holding steady for a few and maybe backing off on the final one. Last squat workout was 5x245, 5x275, 5x285, 5x295, 5x295, 5x295. If deadlifting, I'll do something similar. Some days, I'll kick up the weight for singles, occasionally I'll work sets of 10 or 20. Then I'll hit something like bench press or overhead press with a similar pattern before wrapping up with some combo of kettlebell swings, pull-ups, abs, curls, dips, etc. No cardio or running. We go for plenty of evening/weekend walks in our 'hood.
I tried working in grip training a year ago, and that just caused elbow tendonitis to flare up.
Joints are all doing fine despite past abuse thanks to glucosamine chondroitin.
FWIW, I'm 43, 5'8", 175#.