Tiffany,
Sorry I did not get back to you last night. Like the other posts said, you nitrate problem with the 55 gallon tank is due to the crushed coral, the bio wheels, and waste products. The DSB will help a little, but not that much (in the 55 gallon tank.. Just to much bio load to make a big difference). Best options outsite of getting a larger tank are more frequent water changes, fewer/less feedings, and put in a refugium with macro-algea like caulerpa in it, these will help remove the nitrates.
How often and how much water do you change in the 55 gallon? Do not move your fish to the 20 gallon, leave them where they are, and set the 20 gallon up for the reef tank.
I would recommend the live rock in the reef tank, the 20 gallon. It is not that live sand does not build up nitrates, it is that in a DSB, you have 2 basic types of bacteria, nitrosomonas and nitrobacter.
As fish and invert give off waste products, it quickly changes to ammonia, the nitrosomonas bacteria convert ammonia to nitrite and nitrobacter bacteria convert nitrite to nitrate. Nitrates are then converted in to a harmless gas. Live rocks also aid in the process of removing nitrates as do macro-algaes.
I would recommend using powerheads in the reef tank to keep the water circulating. If you have any more questions, just keep posting them. Nitrates should be not higher than 60 in you fish tank, and lower would be better. Nitrates over 60 can sometimes be fatal to fishes.
Best of luck.