Due to a shoulder injury I need to start shooting the Tyrolean stocked Martini schuetzen shown below.  I don't have to lift my right elbow as high as I do with my Stevens 45.

But first I need to do some load development, which calls for bench work.  This thing is really uncomfortable off the bench, so I want to fill in the Swiss butt with something resembling a recoil pad. 

I know I can just cut up a bunch of closed-cell foam and tape it to the stock, but I was hoping someone here would have a more elegant (and practical) solution.  

Any suggestions would be appreciated.