I don't have firsthand experience cleaning seriously soiled
BCC chips, but I have some in my collection that appear to have been damaged by a prior owner cleaning them.
So far as I can tell, the edges of
BCC chips are sensitive to heat and possibly moisture. Perhaps the combination of the two is what causes issues. The chip itself may remain flat (as opposed to the Pringle warping we sometimes see in Paulsons), but the chip edges will take on a "C" shape where the top and bottom on the chip stick out further than the center of the chip. Think of it as the opposite of the rounding that you would see on a worn chip. If you clean with water, especially warm water, be very cautious about the temperature and duration of exposure. The warping has a negative effect on the feel of a barrel of chips. I imagine chip shufflers would dislike it.
I also have
BCC chips whose color has been altered by cleaning agents. I don't know what agents specifically, but the fading is enough that I won't mix those chips with the others in my set.
Even a magic eraser is going to be abrasive to the chip and could alter the feel.
For spot cleaning, I prefer a damp rag or a magic eraser if you must. One chip at a time while watching TV or something. If you're looking to remove color transfer from a bunch of chips, I recommend trying with a single chip first using least detergent, lowest temperature, and shortest duration in the ultrasonic that works. A dirty chip can always be cleaned, a warped or faded chip can never be restored. I personally wouldn't risk it. As
@Thomacetti said, elbow grease is the best option. Slow and steady wins the race.
When it comes to oil, a little oil goes a long way! Getting oil under the inlay is bad news. You'll need less oil than you think. If the chip is glistening, you put way too much oil on. A few drops on a rag will handle many chips.
I hope that helps!