Here's my story: I have a 26" wheel that I have built with a bmx flip-flop hub (one side threaded for english fw, one side metric). The original axle that came with the hub is a sealed axle with smooth seats for the hub's R6 cartridge bearings. The problem is that this axle is not long enough for mtb spacing (it fits flush with the edges of my dropouts, like a qr axle would, but it solid). An unsealed 3/8" axle will fit in the hub but there is a tiny amount of play between the axle and the inner surface of the bearings.
I have tried using makeshift shims (aluminum can slices) to take up the slack but they seem to be a poor solution that won't offer any sort of reliability. I've also thought about using the original axle and modifying it to work by cutting the axle and using axle extenders but I'd like to avoid this if possible.
Either I need to find a way to modify the original axle to fit my dropouts or I need to make an unsealed axle fit snugly with sealed bearings.
I guess this is what I get for trying to build a mountain bike wheel with a BMX hub, but the wheel is built so I have to make it work somehow. I am asking for any and all feasible suggestions to fix this problem.