If doesn't matter if you have a ptg for soft paints. It only tells you how thick the paint is, not how soft. If it's been resprayed you wont get a true reading anyway really.
I wouldn't even touch jap paint with a polish, never mind G3 and a mop. I would use a DA with a finishing pad and a paint cleanser with mild abrasives.
As said Super resin polish is spot on for paint like this. It's a great product aswell. It has mild abrasives and fillers in it. Going over by hand say 5-6 times on the whole car would see a massive reduction in swirls etc.
Just my two pence. Not like I do this for a second job or anything