The 396th BS(M) was an element of the 41st Bombardment Group (Medium) which was assigned to Seventh Air Force in the Pacific. 396th Bombardment Group (Heavy) trained replacements in the States throughout the war. 396th Infantry was constituted as an element of 99th Infantry Division, but never organized (the regiment was disbanded when infantry divisions were triangularized early in the war).
A transfer from the Air Corps to Ground Forces - even only for the purpose of returning to the States - would have been highly unusual (and extremely improbable).
As stated earlier, he was most likely transferred to 17th Airborne Division for the sole purpose of returning to the states. The 17th was returning to be inactivated so there would have been no reason for airborne or glider training.
As for the invasion participation credit. There were 24 airborne and amphibious landings for which the bronze arrowhead was authorized. Six took place in the Mediterranean Theater (three in Italy).
Seems the farther you go with this, the more confusion develops. Might be a case of "too many cooks . . ." I think I'll withdraw.