I Have A Few Questions About Cleaning

I am not an expert on the subject, but I would reserve that one for very encrusted ancients or detector finds.

I use regular GooGone in my ultrasonic cleaner and it works well but Lindner's Coin Cleaner (much more expensive) worked best.

Be very careful with an ultrasonic cleaner. The coins MUST be in a plastic basket and do NOT allow them to contact one another (if you have more than one coin in the basket at a time). I use toothpicks to separate them.

Many ultrasonic cleaners have metal surfaces that will destroy your coins and these must be avoided.

If they are too far gone, experiment with your idea.... otherwise, I wouldn't necessarily try the method you're using.

AAHHHHHHHHH. To start with please try to remember that dish soaps are all different. Some contain materials that will really mess up your coins. Dish soaps are manufactured differently so that people can purchse the ones they THINK works best. If they were all the same, then there would only be one manufacturer.
When you say water, remember, that too is different under different situations. Tap water can contain Flourides, Chlorides, etc. If well water may contain almost anything on Earth. If run through a water softener, now contains NaCl.
DO NOT use those types of cleaners on coins.
Most types of electrolictic methods do more damage than good.
As to VINEGAR. Only use this if your planning on adding your coins to a salad. Makes for a nice crispty, crunchy touch.