Here is my opinion on this, some of this has been stated, and maybe you already figured out what will work for you, but...
First, cut your feeding to a minimum, which you have already done.
2nd - Get rid of the sand, if you really want to keep a clean tank then go bare bottom. To go bare bottom you will have to increase the flow in your tank to make sure all of the detritus gets suspended into the water column and eventually removed from your tank. For me, this was a project in my 38g, but it meant keeping my livestock in a smaller tank with some of the rock for a bit, the rest of the rock went into a bucket for a week or so. I ended up drilling the tank for a closed loop. I have plenty of rock in my tank, with some chaeto, my nitrates are not detectable.
3rd - you need to work on getting your phosphates out of your rock. Since your tank is established and have fish, cooking your rock outside of your tank is not an option in my opinion. So here is what I would do.
1. While you are going bare bottom. Clean all of your rock with a power head, getting as much gunk out as you can. Make sure to perform water changes, I had a few step process. I would blow off the rock, shake it in another bucket and put it in clean water.
2. Invest in a great skimmer
3. Since you are bare bottom, use filter socks in your sump to catch all of the crap that is going to be in the water column, but make sure to clean it every 2-3 days.
4. Use a Phosban reactor with GFO , I do not agree with the people that say its a band-aid. So are water changes, adding supplements and running a skimmer. Personally, I like to have fish that are fed and not aggressive because of lack of food.
5. Take a turkey baster and blow off your rocks every day.
6. In your sump have some macro, chaeto morpha is good.
I had a similar fight where my rocks were keeping p04. My levels were only .5, but they were still there. By using these methods I have reduced my P04 to readings of 0. Of course 0 is not real, because of nutrient uptake from algae, but I have very little bad algae in my tank.