I have experimented with plastisols, urathanes, silicons etc for about 20 years. I am pretty knowledgable but I do not know everything.
First, when working with plastisol, the harder it is the more difficult it becomes. It bunrs much faster, it is much thicker, it cools and thickens much faster. What this means is, it has to be super hot to even make it pourable. Well because of the hardner it burns much easier. See those two thing are conflicting. you are talking about much harder then a hard saltwater type plastisol. Also the harder the plastisol, the less oil is in it. That means it doesnt float anymore.
Would it be impossible to make your frisbee out it? Probably not impossible but most likeley extremely difficult.
Some suggestions.
There are additives you can add to most materials to make them float and alter their flexability. However floating additives will make your product opaque.
You just might have to compromise one of your criteria.
I suggest you you go to smooth-on and sil-pak and speek to their techs. If they can not answer your questions then you may not be able to make you disk they way you want to.