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How about making a spacer to fit on the spine, all the way from the swedge to the handle? I have used oven bake clay called Sculpey (bought at Wal-mart's craft dept) for similar, with great results. Once hard, just tape it to the blade and form as usual. That way you'll get a gap all the way for the heel of the swedge to slide into.
My press consists of a 6" bench vise with an 18" long x 7/8" dia. handle, and foam sandwiched between two thick aluminum plates. Pretty much hand of God too. I have to be careful that I don't torque it up too much, or the dimples on my Busse sheaths are way too deep. Try the Sculpey - your press won't damage it at all. It's cheap and easy to use. Harden it in your toaster oven.