Model 7 recoil management

Find someone with a 375 Chey-tac, ask to shoot it w/o the brake. That should fix your Model 7 recoil problem.
 
You mention that it seems too short already. If the LOP is too short, that will make the problem worse. As mentioned, try a slip-on pad and see if a longer LOP helps.

A longer, heavier barrel will help but is an expensive option. I'd opt for a heavier stock first as it's likely far less expensive. Think about a thumbhole style if you want to decrease the jump even more.
 
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