Let your site's weeds lead the way. Pull all the grasses and woody volunteers. After that, you're pretty much left with the herbstory, which generally stays under 1' and is easy to keep hoed/chopped off of your crops. Don't rule out annuals - they are perennial in their own way, springing up from seed in every gap of the canopy. Here in Portland, I have clovers, prunella, veronica, violets, wood sorrel, chickweed, scarlet pimpernel, poppies, scotch moss, (yes) mints and strawberries, field madder, arugula, radishes, beets, cilantro, borage, quinoa/millet... all (near)self-propagating every year. I keep a shaker of collected seed that I sprinkle on every bare patch of dirt.
I know you said it's not all about the nitrogen-fixer, but really it should be the foundation of any ground-cover in disturbed sites (annual vegetable beds). I know you said White Clover is too aggressive for you, but you really have to give it a chance. It is everything you wanted in your list of worthy attributes. Much less aggressive than mint, but still resilient. I haven't had much trouble with it overtaking my plants, but I'm also wandering around with a hoe and clippers most evenings of the growing season... And I don't expect too much from any given foot of bed; they should actually be categorized somewhere between vegetable and herb beds... Herbs are much more at home in this kind of situation, so don't be shy with kitchen herbs; they are the best bang for your DIY-buck compared to supermarket prices. Sometimes, for a little extra care, I cut a slot to a hole in the center of a piece of cardboard (1-2' square), and slide that onto the crown of a plant - pretty quick and easy root-zone weed-barrier mulch.
To get big, juicy vegetables takes a more active disturbance regime of soil amending and irrigation. But the ones that had to fight the ground-cover and search deeply for water, they may be smaller and blemished, but I wager they carry at least as much (and probably much more) flavor/nutrition as the equivalent big-juicy (water-filled) specimens.