I did a build for a fellow in a wheelchair that was almost the same. The action was a very nice Winchester Mod 70 short.
The barrel was a Green Mountain replacement Mini Gun Barrel, new in the white. It had a 1-12 twist rate and was 1.125 OD. Picked them up from Barry at Bits of Pieces over ten years ago.
He wanted the same thing you do. Something with lots of punch for close in shots and he could handle an old Savage 99, loaded with 180 grain bullets quite well.
Remember there isn't a lot of give, when it relates to felt recoil, from a wheel chair.
So, I checked out the velocities of the hand loads his brother had made up for the Savage 99, which was a take down whoes barrel had been cut down to 19 inches.
Velocities with Varget over 180 grain bullets were right at 2400 fps, with very little muzzle flash.
So we duplicated that load in the 308 Win case, which is in the low to mid range in most manuals.
This load 41.5 grains of Varget over CCI250 primers under the 180 grn Roundnose Speer bullets he had on hand gave him an average 2435 fps out of the 20 inch, finished length barrel we installed on that Mod 70 SA.
I wanted to profile the barrel of at least cut steps to lighten it but he loved the extra weight and it helped to hold the rifle steady. After all, he wasn't carrying it.
To be honest, I wasn't expecting that barrel to shoot as well as it did. But the fellow shooting it was getting moa groups out of that load almost from the first shots.
He was a happy man.
He wanted to move away from the lever action, which had been a gift from his deceased father, before he had the bike accident that confined him to a wheel chair.
He found it awkward to cycle the action while in his wheelchair.
It's close to what you're looking for but you may have to tune the load to your rifle.
