Dissolving Aspartic acid in vinegar?
The good news is there is no good reason to add vinegar to your aquarium.  You are correct that if you did, the addition of hydroxide to maintain proper pH would then neutralize acetic acid to acetate.  

You can dissolve about 4.5 g of aspartic acid into a liter of neutral water. I assume you try to keep your saltwater tank at a pH of around 8.3 however, which should significantly increase it's solubility as aspartic acid is acidic, having a pKa of 3.9. This is the reason you could not dissolve the aspartic acid with 5% acetic acid, which still pretty acidic with a pKa of 4.8.  

So the solution is to just use the slightly basic aquarium water itself, plus a dose of patience, to dissolve the aspartic acid. You could place it in a tea-bag next to your aerator or something if you wanted to isolate it and see how quickly it dissolves.