I just sold my Burke Millrite after getting a good deal on an Ex-Cell-O (Canadian BP sized). Never thought I would sell the Millrite, it had always done everything I needed, the replacement was just too clean to pass up. Best thing I did to the Millrite was add a digital readout to it, completely changes the usefulness, speed, and accuracy of the machine.
I used to go after everything with Purple Power or other sodium hydroxide based cleaners, but after wiping out more than one paint job with them I have gone back to simple green and reserve the sodium hydroxide based cleaners for when I know I may be repainting.
Your asking for something stronger than Purple Power, that would be paint stripper. Heated sodium hydroxide based cleaner is what is used to degrease parts before plating, so if that's not cutting it you may need to look to refinishing, but that probably not necessary.
I would recommend simple green and soft scotch brite to preserve the factory finish. You will need to work down the grime in layers, putty knives are your friend. This is actually weaker than what you are currently using.
You can keep with the purple power and use the green scotch brite but it will more than likely remove any gloss in the paint, if not all the paint once you get below the crud.
Post up some pics of the stubborn areas and congrats on the mill!