Doesn’t the Boxford have tapered roller bearings, not split shell bearings?

The best way to remove the outer race of a roller bearing is to run a bead of weld (arc or MIG) around the inner face of the bearing race. When the weld cools and contracts, it pulls the race with it and the race will fall out of the hole.

Otherwise you have to use a hammer and mild steel drift and tap the race out, working evenly around the diameter to the race does not kick over at an angle.

If the headstock casting hole is stepped and does not allow you to get a purchase behind the bearing race, and does not have removal holes or cutouts provided, you really have no choice other than the welding trick. Any local welding shop etc should be able to do it if you take the headstock in to them.

New races can be pulled in with a length of threaded rod or long bolt and suitable round discs.

Make sure you have suitable new bearings in hand before destroying the old ones. The “proper” high precision bearings are hideously expensive (P3 or P5 etc). But standard bearings of the right size will work just fine for home hobby use and are much cheaper. Use only good quality brand-name taper bearings such as Timken, Koyo or SKF sourced from a reputable supplier. Lots of nasty fakes online.

And note that some of the very early Boxfords used old inch-sized bearings that can be hard to source today. So be sure you have replacements in hand before trashing the old ones!