If those were his words, "no problem shooting modern low brass", he is not the man to listen to. The height of the "brass" has absolutely no bearing on the pressures produced by modern shot shells. Aside from that, the majority of factory ammo today is loaded to or close to SAAMI Max to allow for proper function in semi-auto shotguns. There are only two companies that I am aware of loading lower pressure ammo for vintage guns- RST and Polywad.
Does your gunsmith have a barrel wall thickness gauge and, if so, did he provide you with minimum wall thickness measurements of the barrels and where they were located along the length of the barrels? Did he use a barrel bore gauge to measure the bores of your shotgun? In addition to a visual inspection of the barrels, these two things are imperative in evaluating barrels on an older gun.