I totally agree with everything you said, except
This can be quite tricky. In my experience, 8 out of 10 cats showing their belly just mean to show they trust you and are happy but do not want their belly touched. Right now I’m sitting the two loveliest, most gentle cats I’ve ever met and they are the first to fully enjoy and even demand belly rubs. Both of them. I’m fully confident they won’t scratch me. I’ve looked after a couple of other cats that wanted some kind of belly contact, using my arm as a toy, but not belly rubs. I had to be careful, though, because when they were enjoying this game, they started licking my arm or hand and, after that, it was love biting, most of the time very soft, but it could get tough if they got over excited.
This morning, I really had a laugh with own of the cats. I was rubbing her belly and she got over excited and, for the first time in a week, tried to mimic a love bite but she really is so gentle that she only opened her mouth and got close to my hand but did not even touch it. She did it several times. I’m amazed!
The only thing I would add to your wise tips is that, after giving them their space and having established a bond, we can explore their likes and dislikes. Sometimes a sitter can find things they enjoy and the owners didn’t know. I had a sitting recently where there were no cat toys, the owner said he was not interested in toys. I bought a small toy and tried. It turned out he was a slow player, he turned around showing no interest at all and hid somewhere, he wanted to pretend he was not interested and then “attack “ the mouse by surprise.