It was claimed that JB removes metal all the way down the bore. Easily proved by periodically measuring the barrel inside diameters. Or observing faster accuracy degradation which didn't happen with my barrels.
If anyone can prove it damages the bore, tell Brownell about that.
https://www.brownells.com/gun-clean...mbedding-bore-cleaning-compound-prod1160.aspx
If
used as directed, no it will not damage the gun. But it is also important to understand what it is, how it works/cleans.
Is is a mild abrasive intended to scrub out stubborn copper and carbon fouling. Abrasives don't chose what they work on. If you out it down a squeaky clean barrel it will turn black, indicating it polished, abraded the barrel surface.
JB is applied on patches from breach to muzzle. If you are applying it to the entire bore, and is is an abrasive it will remove metal from breach to muzzle. No empirical data or measuring needed. How much, not much I suspect, but based on how it works and where it is applies it does.
In regards to the OP. I think the gun will be fine. You stated about 200 patches of which abut 1/3 were JB bore past meaning approximately 66 patches. While not ideal this is only equal to about 6-7 normal cleaning sessions. I doubt you harmed anything but I would not recommend going that aggressively on a normal basis.
Get a cheap bore scope. See what is actually going on in the barrel. get a good bore cleaner preferably one that works on copper and is bore safe (no ammonia)
I am partial to bore tech eliminator as it works on carbon and copper. you can let it soak as long as you want and it will not hurt the barrel. The thing with it is it will react to brass jags and copper/bronze brushes so you may need to get a fancy jag and a nylon brush. With heavy copper fouling I have found I needed to go through the cleaning steps 2-3 times letting it sit about 30min to 1hr between sessions to get the bore back to brand new.
I use the bore paste and bore bright as a finishing step after normal cleaning if I have any stubborn deposits that just down want to come off.