+1 for the risks attached to contraction after welding.
IF the shaft can be pressed through the bearing, (IF not you won’t have much option but to saw it off to get it out, even if it means destroying the bearing. That can be replaced)
Once out,, if the shaft will pass through the Headstock (Use a steady, if it won’t) it can be turned down until it JUST cleans up.
Then turn up a sleeve, back to original OD, with the bore having a slight interference on the turned down shaft diameter (Say 0.0127 mm smaller). Then fit he sleeve into position using the “Heat and Freeze” tecchnique. With the shaft at -18C, it should fit onto the shaft at about 200C.
If the shaft is too long to fit into a freezer, you will have to heat the sleeve to a higher temperature, and press into place. For this, to minimise damage to the sleeve which will be softemed by the hight teperature, use a dolly to take the pressure from the press.
Oncve everything has soaked back to ambient temperature, you should be in a position to reassemble, and make the machine useable.
Howard