Opie,
Here is one of the problems you are facing as far as strength of the barrel is concerned. You can't see how well (or how poorly) the rifle barrel fits inside the shotgun barrel anywhere along its length except at each end. How many gaps might there be along this length that you can't see? It's unlikely that the rifle barrel was originally made the exact OD of the bore of the shotgun barrel. So, how was the fit made? Was the rifle barrel specially made to fit inside the shotgun bore? Was a rifle barrel that was close in size used and some type shims made? These are all questions that I don't know the answer to.
Unless the rifle barrel is a PERFECT fit inside the shotgun bore, then it's likely that the shotgun barrel provides no strength against rupture of the rifle barrel. The reason I say this is because without a perfect fit, each barrel would act independently in the strength department. If the rifle barrel, which should withstand pressures in the neighborhood of 45K to 50K psi, should rupture, then the pressure is going to go right on through the shotgun barrel (max pressure of about 18K psi) just like it wasn't even there. Only if they are a perfect fit and even the slightest expansion of the rifle barrel would be resisted by the shotgun barrel will the shotgun barrel give any protection against rupture.
Of course, if they put a perfectly good rifle barrel in there to start with, then it doesn't matter what the shotgun barrel does, if anything. But that's the question. How good is the rifle barrel by itself? I don't know.
You could always rig up a way to test it by using sandbags and a long string to pull the trigger. If you do this, be sure to allow the gun some room to recoil some or you may crack the stock if you put the butt up against a brick wall or something similarly immovable. Even this wouldn't necessarily tell you if the gun is safe with numerous .444 rounds unless you put a couple of "proof" loads through it. It might work out great, and proofing it yourself may be the only way to know for sure.
As for converting it back to a shotgun, that wouldn't be my choice. I would use it as is, if I could prove it's safe, or buy another barrel to shoot shotgun shells through. BTW, you might be able to shoot .410 shells in it. You would just have to measure the chamber and find out.