You need a competent person to properly measure the bore diameters 9 inches from the breech end and see if they match the proof diameters. Then, if your barrels aren’t pitted, dented or otherwise damaged and your bores haven’t been bored oversize your bores would be in proof as originally made, a moderately honed bore can still be in proof but a .010” overbore takes it out of proof. However if this gun was originally chambered 2 1/2” (65mm - 67.5”in Europe) and the chambers have been lengthened and the gun not reproofed with these longer shells and so marked the gun is no longer in proof for any ammunition. Then wall thickness becomes important, particularly at the area that was at the forcing cones of the original chambers, where material was removed to lengthen the chambers. This is the point of highest barrel pressure and both the thickness here and the strength and elasticity of the steel are critical factors. Not knowing the qualities of the steel used in these barrels the only known factor affecting strength at this point is the thickness of the steel and I don’t believe there is any specified minimum thickness, it’s usually an experienced judgement call well tempered by caution, most experienced shotgun smiths will decide on a case by case basis. Bottom line, if it’s in proof, including original chambers, and in excellent condition go ahead and shoot it with appropriate ammo but avoid heavy loads in deference to the age of the gun.
If as you suspect, the chambers have been lengthened, then it is out of proof, no argument. And you can not get a certified proof in North America. A very competent shotgun can inspect and measure your barrels and could recommend whether it would be safe to shoot and with what but these are only his recommendations, he has no control over what you decide to feed it. Many many old guns with lengthened chambers are presently in use, probably some of which shouldn’t be, most are fine but a few could be a ticking time bomb and without professional assessment nobody knows.
Yes, Stuart Newby is still in business, semi retired and very selective about what he does and who he does it for these days. He has a superb shop but has no store front and actively discourages visitors. At this time he is probably the most experienced and skilled English trained gunsmith in Canada and he can properly measure and assess your barrels. He will tell you what you have and give you his trained opinion of what you can do with it. He won’t put ‘proof’ pressure loads through it and I’m sure he will discourage you from trying this as well. If he takes you on as a new client he will give you a time estimate for this and normally his turnaround on most jobs is very reasonable.
If your gun passes inspection it must be considered capable of indefinitely safely digesting any ammo that fits, it can’t be assumed that you or all the owners that follow you will only feed it special low pressure ammo, someone someday will be using off the shelf ammo of unknown but likely high pressure. For your own use your low - moderate pressure handloads are obviously safer and they have the added advantage of easing strain on an old treasure, greatly extending it’s service life. J.