I have a number of guns similar to your Sumner.
I mostly reload 7/8 oz or 1 oz loads to about 7000psi.
I have a Henry Atkin backaction hammergun from about 1885.
It has the original damascus barrels as well as a set of pre 1900 steel barrels.
I use this gun a lot for sporting clays, skeet and bird hunting. In addition I do gunning for field trials and hunt tests and dog training.
I use the reloads mostly practice and dog training.
I buy shells from PolyWad, RST and B&P as well.
All have pressure data for their for their ammo. B&P have several low pressure loadings that are very soft shooting.
The Atkin has been reproved similar to yours.
I am not concerned for the barrels as much as the action.
Shooting shells that are high pressure will cause the gun to get loose. That can cost $500.00 or more to fix.
I shoot several thousand rounds a year in the Atkin so pressure is a big concern.
So far I see no indication of any wear on the hook after at least 10 years of use.
Most of my other old guns don't get a lot of use so there is less concern.
I do recommend the spreader loads from PolyWad and RST if you have a lot of choke.
I use the Poly Wad spreaders when I shoot in chukar time trial competitions. These allow me to put a bird on the ground very quickly without excessive damage. My dogs don't like to retrieve blown up birds.
The Atkin is choked .008 and .016 and I can put a pointed chukar on the ground in less than 10 yards with the spreaders out of the .008 barrel. If I need the second barrel I might as well walk off the field as I would have no chance to place in the event.
Hope this helps.
