The wheel keyways look OK in those photographs. If that is correct, you only need a solution for the Woodruff keyways in the axles.
Long ago I knew a guy who had the same problem with a more expensive component: a Woodruff key in a vertical shaft driving the overhead camshaft of his 1937 MG NA. He silver-soldered the key in place. As my father predicted at the time, it lasted less than a week of driving to work. The bearing pressure silver-solder can stand is very low. Bronze would have had some chance. A good gas welder using mild steel filler could fix it permanently, but it would be hard work hand-filing the shaft on the two sides of the key to make it fit the hub again: probably a couple of hours of careful work, involving many expletives. (This was not a feasible solution for the MG - the vertical shaft was also the armature of the generator, and the windings would not have stood the heat). I think that kind of welding is a feasible way to repair it "as good as new". What I think I would do myself, is make a "stepped key". You would have to get someone to mill out the damaged keyways in the shaft to a greater width, so they were perfect again. You would buy or make Woodruff keys of the new width but the original diameter, then mill or file way part of them on each side to fit the hubs, so that each key would be thicker where it fitted into the shaft than it was where it fitted into the hub. My father taught me that trick long ago, when I had the same problem as you have, with one rear axle of a fairly rare model of 1937 Austin. He made the replacement key (a rectangular one, not Woodruff, IIRC) from high speed steel, so it wouldn't break again. (It didn't - thus losing me an argument. I had bet that the lower impact resistance of the very hard HSS would result in brittle fracture).
