Cyber, I've let several people at the range try out my 375 H&H's. Almost all of them have commented that it wasn't as bad as they thought. Only 1 has asked to shoot another round of my 416. None has shot my 458 Lott more than once (of the few that would even try).
I would think that if you are shooting 60rds of 7mag you probably could move up to the 375 H&H without too much problem. I would start by shooting a couple rounds offhand and if you don't mind that too much proceed to the bench or other positions from there.
A 375 short mag might be an interesting round, but the other 375's available IMO vary from Very Good to Greatness, you ought to shoot one. If you are going to be near Oklahoma City anytime soon PM me and maybe you can meet me at a range and try one of mine..........DJ


Remember this is all supposed to be for fun.......................