You have to describe your system a little for us to help you. For instance, if you have an overflow and a sump, you can buy a low micron filter sock (1, 5, 50 microns) and put it in your sump whenever you turkey baste your rocks.
You can also buy a canister filter with a micron filter and run that periodically when turkey basting if you don't have a sump.
More flow will help to a large degree but no amount of flow is going to stop all of the detritus because not all of this detritus is getting there from settling. A lot of it is actually coming out of the rock itself. Bacteria are pushing it out of the rock by bacterial turgor (pressure). It is good that you are turkey basting because the junk that the bacteria push out is nutrient-laden algae food.
Okay....with all of that said. Most of us are guilty of two things.....overfeeding and not basting often enough. More food equals more uneaten food plus more fish poo. Regularity of turkey basting also has an effect on how much snowstorms we have. We can't control the bacteria inside the live rock but we can control these two issues.