Roger, not chrome lol
I like evaporust or electrolysis for rust removal because it shouldn't 'move' the good metal around. For example, you shouldn't have any raised areas on your column to cause issued during table movement etc. Abrasive rust removal and roughen the surface thus raising it in some areas.
You can tape together a cardboard box that's close to the size of the parts and put a garbage bag in it to fill with evaporust. That way you don't need as much liquid.
Either way, I think the painted areas look ok. I like the old patina myself. Were you planning on total tear down to rebuild the quill etc? If so you could address the indivitual pieces as necessary.
Nice old drill