I have pressed hats for 25 years. Not as many in the last ten years. With plastisol, I pretty much limited myself to five panel hats.
With a little fiddling you could cover your platen with some neoprene or mouse pad rubber, or something that allows you to cut a channel. You can hold this on with some of the 1/4" heat tape most transfer places sell.
Vinyl is more forgiving, but even so, some covers more invisibly than others.