I do have both, but none in front of me right now. I will say that while your idea is novel, I don't believe it will work. The SHBM is lighter than the FBMLE. There are also differences in balance due to weight differences. The FBMLE also has a fair amount of curvature in the handle. I don't think there is enough steel there vertically to make an FBM handle into a SHBM handle. What's more, even if everything I said was not true (but it is), I think you'd be removing so much metal from an LE that the chances of something going wrong are fairly high. Uneven grinds and destroying the temper are just the begining of the possibilities.
IMHO, you would be light years ahead by finding and buying the real McCoy.