Agreed with Allan: Make a new shaft. If you try building up the worn shaft, you will likely wind up chasing your tail as welding will cause the shaft to bend or wind up with a bow (or two), or a dogleg if you build up close to one end. Sometimes, a bent shaft can be reasonably straightened using "flame straightening". This requires an oxyacetylene torch with a brazing tip to put a concentrated heat (usually to a dull red heat in dim light) in one area and using either water or compressed air to cool the area that had been heated. This shrinks the area which had been heated and can draw a bent area back to straightness. It requires a bit of instinct or a gut sense, a good eye, and patience. For something like the shaft on your Diamond milling machine, I would just get a piece of something like Stressproof 1141 shafting steel and make a new shaft. Stressproof is quite strong, machines beautifully, and is manufactured with a drawing process to create a grain structure that allows all manner of machining without distortion. Cold Rolled Steel is not what I'd use. If you machine "assymetrical" parts from cold rolled (such as milling long keyways), cold rolled will "self relieve" and distort. Make a new shaft, make sure to put fillets (radius's) where the shaft changes from a larger diameter to a smaller one, and the mill will be fine.
The weight of the Baldor motor was unlikely to cause the bending. In the era that your milling machine was manufactured and first used, electric motors were considerably heavier than that Baldor motor. Someone mis-handled that mill in moving it: could have ran into it with a forklift, or rigged it improperly to lift it. Bent shafts such as you describe do not happen due to an overly-heavy motor.
John Oder is correct: when you own and work with old machine tools, you can expect to "reverse engineer" and make parts for those old machine tools. If you do not have a working milling machine, make two shafts instead of one. Install the first shaft using shallow drillings in the shaft for setscrews in the pulleys to seat into. Use the mill to machine the keyways in the second shaft. Then, swap out the shafts so the one with the keyways gets used in the milling machine permanently. Use the original shaft as a model to take measurements off of to make the new shafts. It all plays into developing skills in machine shop work, and these include what we call "reverse engineering", designing a new part to fit where the original is either damaged beyond repair or simply missing. Setting up a milling machine to cut a keyway in a shaft is a basic exercise and will teach you quite a bit in the process. Plenty of keyways were cut on horizontal milling machines before vertical milling machines became commonplace.