For several seasons I shot an 8K "LUP" load through a Birmingham black powder proofed J P Clabrough Damascus barreled double with no problems whatsoever. Load was with the then New "HyScore", not 700X & used 1 oz of shot @ about 1150 FPS.
Nota Bene (Note Well) that it is shot payload & velocity which affect the stock, PSI has virtually nothing at all to do with Stock damage. PSI essentially affects only the "Max" chamber pressure, which affects only the chamber area of the barrels.
Any barrel beech which will not handle 7K-8K psi needs to be hung on the wall or at least confined to light loads of Black Powder only.
Operating the loading press will condense the powder in the hopper. Check weights should be taken while the loader is in normal operation.