To answer your question, no. You cannot increase your own summoned food quality, that's the best it gets. But when you are deep within a zone and don't want to go back to restock, it's better than nothing.
Stop by the Outfitters Cabin in central Antonica. Upstairs you'll find a pleasant lady named Matsy Rollingpin, she'll give you some simple quests and hand you some good chow upon completion.
You can also zone in to the various piers and get better food/drink from the merchants. The piers at Thundering Steppes, Nektulos Forest, and Zek have merchants that sell higher level food. In fact, I exclusively used food from the Zek merchant for levels 38-50, and it served me fine.