The plastic follower for the action spring in the receiver was intact as per the last video. While I agree with you on the solder, I'm fairly certain that polymer would be done for long before the steel was damaged. I'm sure he will be careful, either way - there are plenty of ways to go about this safely without discounting it out of hand.
Only way I know of would be to get the barrel hardness tested. But based on the amount of half-burned logs I've seen laying around campfires the morning after, fire can be wildly different temperatures in just a few inches. The barrel might have been baked hard while the back end was not.
There's two ways to know for sure.. Doing hardness testing is the only for-sure way to know exactly what it's at, but it'd need to be done all the way up the barrel and you'd either need to know (from the factory) exactly what alloy was being used and what the hardness should be.
If it were me, I'd bolt that bad boy down to a bench when it's finished, tie a string around the trigger, hide behind the truck, and yell "HEY Y'ALL WATCH THIS!" as I pull the string a few times.
But I'm a reckless type who likes to blow things up "just because", and don't mind patching a leaky truck radiator with bubblegum to drive back home. So I'd probably do the latter. But that's just me.