Usually the only difference between a park flyer rx and a full range one is the number of antennae. Park flyer rx's typically have just one active antenna which means you increase the change of losing signal. Not usually a problem close in where you would lose and regain the signal without noticing...worse at range where you might lose signal for longer. Two antennae at 90 degrees reduces and/or eliminates the chance of losing the signal at distance.
I don't know the range of a JR park receiver, but the FrSky ones say 500m. This is fine for an EPP model which would rarely, if ever, get that far away. In short, yes, go ahead and use a park rx in the foamy.
Mike