I have another post I wrote in the 'gunsmithing' forum titled "1st rust bluing project" where I describe my restoration of my BAR and showed linked pictures. I've familiarized myself well with my gun and keep it well maintained.Getting rid of that bulge should help a lot.
Taking 20 inches off that barrel will only reduce your velocity by 50 feet per second, nothing any animal you shoot at will notice.
If you're getting a sore shoulder after firing 10-12 rounds now, you're definitely going to "feel" the 7mm Rem Mag much sooner, likely after the first shot.
Your BAR, because of its action produces slightly less recoil than a bolt action rifle.
If you get moving on your hand loading, you can easily make up that 50 fps safely with that rifle.
The Bar has recoil buffers available for it, if it doesn't already have one. These tame recoil a bit and are easily installed.
These buffers are cheap and available online. Just Google Browning Hi Power Recoil Buffers.
Rather than purchase a new to you rifle, I would either get the bulge removed from the existing barrel or have the barrel replaced.
Cost would be about the same as another rifle to replace the barrel, but you would still have the once fired cases and other reloading supplies already on hand.
It sounds like money may be a bit tight? This is nothing to be ashamed of. It happens to everyone.
That means cutting back the barrel to the first useable distance would be preferrable. However, bulged barrels can be tricky to fix.
What looks like a 1/2 inch or 1 inch bulge might need an inch or two of barrel removed to remove all of the bulged area. This may put your rifle into the restricted or prohibited class.
That BAR is a very decent rifle. They can be dreams to shoot if they're accurate and functioning properly. Maintenance is required.
Good luck with this. Procrastination seems to be your worst enemy on this one.
I think I will bring it to a known reputable smithy near me that I've been recommended to before. See what it costs and what options there are to repair the BAR. I've talked with him before and he said no one makes those barrels anymore do to the design and it's getting hard to find them. He actually suggested shortening the barrel, believe he estimated around $200-$300 if he could find his jig to adapt it to the lathe.