I'm in CA and have restored a lot of machines, including some at least as filthy as your South Bend (a Burr King that was near the exhaust of a grinder comes to mind).
-I use a heated ultrasonic cleaner with Cascade dishwashing powder and Evaporust for everything that will fit in it. Don't ask me why Cascade---I have tried all the usual suspects plus several other brands and had various problems, but Cascade in the green box works great.
-I use Simple Green + SOS (or Scotch Brite) + hot water on everything else EXCEPT MACHINED SURFACES.
-Kerosene will clean old paint without removing it.
-I use a lot of Acetone, too. It is not very bad for you if you get it on your skin, unlike other strong solvents (your body makes it in small quantities). Of course, the leaded paint and grime you dissolve with it will follow it through your skin, so wear thick latex chem gloves (it will eat Nitrile). Acetone works amazingly well---it is an excellent solvent---and is cheap and widely available. Apply it and keep it from evaporating for a minute or so, then watch as the grime magically goes from solid to easy-to-remove. Use it outside to avoid fumes.
But if I were in your shoes with another huge filthy machine, I would be tempted to remove everything with electronics or bearings in it, then have it steam cleaned. Reliable Tool (remember them? huge socal machine tool reseller) used to do this (well, without removing anything) before they shut down---machines from them were always nicely degreased. There are a ton of steam cleaning outfits around here. If you have it on a trailer, then someone with a steam cleaner running can do it in like 4 minutes.
There are also lots of blasting and acid dip places around if you plan to repaint anyways.
So, let's see your lathe
