The old scope is a Bushnell, which I've learned is a brand with not much eye relief. It was recommended I buy, and I did buy, a Leupold, for its greater eye relief. I will just move the Bushnell to a .270 I just purchased.
I'll take a look at the EGW base and the Badger, Talley, and Seekins rings. I assume since they were recommended they will all fit the EGW base.