If you've been "battling green & cloudy endlessly", it's because you're not properly maintaining your chlorine levels, and has nothing to do with your pump/filter problem. However, it's possible that you just have never had enough of a dead algae load on the filter to notice it blowing back through to the pool until now. I don't have a cartridge filter, so I'm not the best to give advice on them. However, all the pool owners I know that DO have them can replace just the cartridges and not have to replace the whole filter ( unless you're ready to go with sand or DE, which are much easier and more efficient to deal with). Try replacing the cartridge. If the cart is bad, that will fix the blowback problem. If the problem continues, then I think you need to be looking for a much bigger filter or smaller pump. I have a 1 HP pump on my 29K gallon pool and it is more than enough.

Janet