How did you fix your problem? I have a PR1000 and a PR600II, but have not tried to use the puffy foam yet on hats.
I think the problem was my lack of practice with caps. The end result here is not perfect merely acceptable. I just hooped the cap very carefully then I sort of held the puffy foam on the cap till the unerlay was stitched. I am sure there are tricks I don't know about but it worked ok.