I think dish soap is a great start. It’s mild and doesn’t have abrasives or harsh chemicals that may stain the watch. I have a Mk2i and that’s how I’ve cleaned mine when it needed it.
You may also have developed a mild allergy to whatever the back of your watch is made of, in which case cleaning won’t help.
No doubt. I pick car every time. Listening to the douchebag cyclist whining after the accident would be too much for me to bear.