Nice score, that 27 is going to be a challenge. I’ve used regular white vinegar to help dissolve rust, by soaking the parts over night. For the old grease I’ll use kerosene in a spray bottle to loosen up the dried out oil and grease.
That zig zag machine has a cool look to it, the 15 clones are certainly good and usable machines. I have an old Japanese 15 and it works great. It came from a land fill “o)