If you don't feel confident in the scarf patch, instead of just shortening both tips, how about trying to make it a two-piece takedown bow with a new limb to replace the one you sanded into too much? I've seen other posts where guys will take a good limb from a bow that failed and make another limb for it. It's a little more expensive than your current solution, but I think it would be better to do that than to make wall art out of the bow.