This is one I'd really like to solve. I've tried a number of bino harness designs and the enclosed ones are just too danged bulky for me. I recently bought the most minimal Alaska Guide Creations harness and I can't bring myself to use it. The padded case and overall thickness of the harness is very obtrusive to me for constant wear. That's no slam on AGC...almost all designs feel that way on my chest. Not a huge deal when sitting in a treestand, but too much for me when dealing with a loaded backpack, warm clothing, sidearm, etc.
I currently use a Bino Saver from Hidden Wolf Woolens and haven't found anything better while being unobtrusive.