Wish I could help with specifics on your Henry but I recently purchased a Marlin 1894CS (.357). It feeds both .38 & .357 SWC without a hitch, fortunately for me. I chose to load .38 equivalent loads in magnum cases to avoid build up in the chamber. As an inexpensive offhand practice/plinking load I am pushing the 158 LSWC at +/- 900 FPS over a starting charge of W231.

If you haven't already tried them, go ahead and run some of your .38's in your Henry. If you already have both the gun and ammo, what have you got to lose but some time at the range? (As if that's a bad thing)