i would put that 1/8" too deep medium on the bottom right above the bottom board and not worry about it. i'm guessing that when you cut it down you cut off the bottom so the frame rabbits are as they were originally.
Best solution. But I have mediums at 6 7/8 with 6 1/2 frames. and don't have a problem. Maybe it's because I get it all from the same source.