You could certainly try sanding down into the filler coats a bit in an effort to determine where in the various layers, or how deep, the cloudy stuff is, but there is no guarantee that it will cure the problem. Stopping at just the right point with a sander that's powerful enough to cut through resin is pretty tricky. You can wipe down the sanded surface with water and while it's still wet, you can get a pretty good idea of how it will look with new resin and varnish on top of it and/or whether it fixes the cloudy resin problem.
Stripping and re-glassing is an awful lot of work and expense, a lot of which is really tedious, back-asswards boat building. It would have to be an awfully good boat before I'd do that. It's probably faster, easier and produces a better end result to just build another one.
As for this one, I'd probably give it a good 100 grit sanding to freshen-up the surface and then give it a couple coats of good marine enamel in some nice color. The very idea of paint freaks out a lot of strip builders, but luckily I built enough strippers that the novelty of the whole "strippy-stripey" thing kind of wore off. Most of the time, I look for a nice profile first. Whether it's red, green or natural cedar strips with little easter bunnies inlayed into it doesn't seem to matter much. It does also offer the attractive option of a couple hours of light sanding and a $25 can of paint fixing the problem. With the other options, you're going to be there for quite a while.