The ops photo shows that the cylinder is a short 38 special. Because it was his Grandpa's I would leave it alone, reamed or not. Plenty of those were reamed to 357 without any ill effects, but not the best plan. If I want to convert a 38 special to 357 I fit a factory 357 cylinder by shortening the barrel extension and re-cutting the forcing cone or installing a 357 barrel. Neither the barrels or cylinders are hard to come by. I have yet to see a frame that let go where the cylinder remained intact.
As far as the 6 rounds with 357 head stamps go. I would NOT use them to see if the cylinder was reamed. They may well have been shortened by whoever gave gramps the "good ones". I would check with known factory 357 brass.
