I ordered some of this:
http://www.tamiyausa.com/items/paints-finishes-60/tamiya-maintenance-material-62000/cera-grease-hg-87099It's easy for me to get in Japan, and both Japanese and English websites talked about it as being highly safe and suitable for both plastic and metal, especially plastic gears. It's originally designed for remote-control cars and electric trains, I think.
My biggest fear is that the yellowing was a result of a chemical reaction with the gear plastic. I am suspicious because I had also put some of the same oil in my JVC X'EYE last year, but when I opened it up today, the oil was still clear. I didn't use as much as I did in my Duo, and the temperature might have been different, but it still doesn't make a lot of sense.
Anyway, what's the best way to clean oil off these gears? I did pretty well with (don't laugh) toothpicks and toilet paper, but I'd like to get them cleaner still. I separately tested dishwashing liquid with the oil I used, and sure enough, that cut right through it. I might try it if nobody else has any ideas.
Here's one thing I've learned: many lithium-based greases, including the white stuff, still contain petro-chemicals which can affect certain types of plastic. If you're doing this in the name of preventative maintenance, be sure you're not doing more harm than good.
I would recommend this to anyone, though. Even with that sewing machine oil, the rate of disc access failure plummeted for both my Duo and my X'EYE immediately after I applied it.