Hi Ravekiss. Sorry to hear about all your trouble with the tank. While I'd definitely go and get the phosphates checked (can't hurt), before you go through the monumental task of removing all your gravel, try this.
I had about the same problem as you -- good filtration, no nitrites, low nitrates, etc. -- and I had cloudy water for almost three months. I just "fixed it" about a month ago, and now the tank is quite clear again. My problem started when I added more light so that I could put in plants that required brighter lighting. I got a serious algae bloom, got a Siamese Algae Eater and adjusted the lighting, and got rid of the algae -- but that stupid whitish haze never went away.
Anyhow, one weekend I made a series of changes in the tank -- I added a substrate feeder, which will push around in the gravel in search of food. I also added an army of ghost shrimp, again to nibble away at any uneaten food. (I don't think I overfeed, but I'm a big believer that there's always some food that "gets away".) More importantly, though, I added some fast-growing plants and I started vacuuming the tank differently.
I don't suggest that you add any more fish, since you probably need to transfer some of the ones you have to a different tank. So a substrate feeder is out of the question. You could probably safely add about 4 ghost shrimp if you'd like (someone correct me if I'm wrong), since everything I've read has led me to believe that they provide a great asset to your tank while having very little effect on your bioload. They will scavenge for what they need to eat, so don't overcompensate by trying to feed the shrimp as well, or your clever plan will backfire!
Try to get an idea of what kinds of plants would survive in your tank. If you don't have very bright lighting, or if you're not sure how bright your light is, you could try anacharis as a start. It is commonly available (around here at least), it seems to grow quickly, and it sucks a lot of its nutrients from the water column. If your problem is high phosphates and nitrates, this should help. If the anacharis grows spindly or seems not to grow at all, you will need a lower light plant. You can post to the Plants board for ideas. If you are sure that you have a fairly brightly lit tank, I'd go for a variety of myriophyllum (a "fluffy" plant -- your smaller fish will probably love it). That's what I'm using now, and it's great. A pretty plant, a pretty color, and it just chomps away at the "extras" in the water. Since I'm guessing that you don't have much experience with live plants, you should know that both of these are easy to plant. Take them home, take the little lead ring off the bottoms, and rinse them well in dechlorinated water. (Check for snails while you're at it.) Cut off the ends of the plants and strip the bottom 3/4-1" of foliage, then just push the stems into the gravel far enough that they stay put. If they end up floating up to the top, just replant them.
Okay, the other tip I have is to make sure that you're vacuuming well. Because no one gives us lessons in this stuff, I guess we just have to learn by experience. I was vacuuming the gravel in the same way you would vacuum your carpet -- by running the siphon tube over the gravel and picking up what was laying on top. I did this once or twice a week, and I paid special attention to the areas where the pleco (poop machine) spent most of his time. That worked very well for a few months. Then I started with the cloudy water problems. The problem was that anything that I didn't catch in the intervening days (or that had settled into the gravel) was now there to stay since I was just doing "surface cleaning".
My suggestion is this -- regardless of how well you think you're cleaning the tank, commit two weeks to cleaning the tank every other day. Aim for a small water change (10-15%) so you don't mess too much with the balance of the tank. Mentally separate your tank floor into sections, and each day vacuum only one section of the tank, but do it really well. Take the siphon tube and push it far into the gravel. Let it sit there until there's no cloudy water or bits of junk coming up through the tube, then move it to another spot about an inch away and repeat. Keep doing this until you've removed about 15% of the water, then call it quits until the next time. Strategically move your way around the tank, vacuuming very well. A benefit to doing this is that you get an idea of where the dirty areas are in your tank -- some will probably be consistently dirtier than others.
Whether or not you add any plants, try the vacuuming thing for two weeks and see if there is a substantial difference in the quality of your water. I can tell you that it made a huge difference in my tank. I think the new plant and the shrimp definitely helped to speed things along, but I think the change in cleaning methods is what has paid off in the long run.
Good luck,
Pamela