Sorry, I've fixed cored fibreglass, but not foam core plastic laminate. How you fix the gouges would depend on the composition of the plastic and whether glass will stick to it. If possible (and on general principles), if you can determine what the original plastic is, patch it with that if you can melt it on without setting fire to the foam core, and then sand it down or simply shape it with a razor.
For $400, you can afford to experiment. Roughing up the surface and having a crack with thickened epoxy is worth a try, but I bet the epoxy is considerably denser than the plastic and might fall off.
If that doesn't work, try gluing rubber or PVC patches on with contact cement, and paint the outside so it doesn't show.
But seriously, I don't have a clue what you boat is made of (there's dozens of structural plastics in general use) and the potential for making it worse is strong.