I cut and welded a trans input shaft, worked decently all said and done. People do this stuff all the time for farm machinery and such, Im sure it will work out well.

You can also just disassemble and cut the axle, put the pieces in a lath, flatten the ends, drill and tap a hole down the center, champher then ends and thread them back together with a piece of threaded rod, then weld it up. Then it should be perfectly straight and even without too much difficulty. Would not be as strong as diesel's method, but both ways would probably work

If you did that, I doubt you would have to bother with balancing, especially at that speed of rotation

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