Actually its not that suprising your nitrates are high. The system that you have has no means of exporting nitrates which are at the end of the nitrogen cycle.
Filtration and the Nitrogen Cycle, by Les Pearce
The normal bacteria buildup in tanks only breaks down ammonia and nitrates into nitrates. Obviously your water changes are not exporting enough nitrates and your tank has been in a high nitrate environment for a while so your rock and sand probably has a fair amount of nitrates locked in.
Even normal feeding will cause nitrates to increase and if you import through normal fish waste is higher than your export - you nitrates will go up and up and up.... From what you are saying it doesn't sound like you are overfeeding. I feed my fish 3x a day.
To bring Nitrates down you need some means to reduce nitrates you may want to think about:
1) Running an absorbent agent like Purigen from Seachem. There are lots of these on the market. I find Purigen is good for smaller tanks onlly - yours (55g) is close to the limit. Start with the small pre-packaged size. This stuff is messy to handle if you are using your own filter bags.
2) Run a refugium with macroalgae. The plants will consume the nitrates and help with the export. You can even get a small HOB refugium if you don't want to bother with a sump. Mangrove plants work too but I don't find them that effective. This is probably the best solution long term.
3) I don't recommend this for you but you can promote anerobic bacteria growth through carbon dosing and biopellets. If you are not careful you can crash your tank with these methods.
If the nitrates are not bothering your fish (they are healthy, eating and active) or corals (probably slow growth at 80ppm but not harm them) - just take you time with whatever solution you want to pursue. You probably do more harm with sudden enviornmental changes.