no...their bacteria is mostly in their filter. Its probably not incredibly helpful to take all the rocks out and clean them...would do just as good to do a gravel vac each water change though instead.
Some people say no to a UGF, but sometimes they work well when you're using it as the 2nd type of filtration in a tank and are sure to keep up with the cleaning. Installing a UGF would mean taking out all the gravel, most people consider that the biggest pain...but it sounds like you're used to it heh and it would definitely be the cheapest option for you to try (aside from giving some of your fish away...). IF you decided to try the UGF route you would no longer want to take your gravel out and wash it. You'd want to vaccuum the gravel while in the tank because as mudracer mentioned, all of those rocks will have good bacteria on them because they are your 'filter media' for a UGF.
Diatom filter...dunno. Dont usually mention them around here maybe someone will pipe up?? If it was a tropical tank I'd say get some otocinclus in there...but they're not coldwater fish and your goldies would probably think they were put in there for a snack
Your other options are HOB filters (like the one you have but all different brands and versions, some are made for huge tanks, other for smaller tanks but basically all the same filter type. They hang on the tank.) or Canister filters...which are usually designed for larger tanks, but basically have a bigger capacity for filtration. The filter part is a big...canister...that sits below the tank level (usually on the floor) with two hoses going into the tank...one sucking water out and pushing it through the filter media in the canster and the other putting it back into the tank. That'd be an option for you, but it is a more expensive type of filter overall. The best type is eheim...and you'll see they're very expensive. I have a fluval 304 on my 46 and its done a good job. Others have a RenaXP and they really like them.
Have you tried carbon in your filter as a way to get rid of some of the cloudyness?
Also, you shouldn't replace the filter cartridge in your whisper as often as the box says...but you should rinse it in used tank water every time you do a change. I imagine with such a high bioload you may have to replace it more often than a more lightly stocked tank though...I usually only replace mine once or twice a year.