I like Nick's idea of looking for the plots that have broadleaved weeds in them. That is really a good indicator of the lack of ick.
I would suggest sourcing as much spent coffee grounds from local coffee shops or diners as possible. Worms go crazy for them, and they're nitrogen-rich, too.
You want to incorporate as much organic matter as you can into the soil, with all the clay you describe, and probably gypsum dust and grit, too. In many cases, impermeable clay will indicate a calcium deficiency, and gypsum will correct that without adversely affecting your soil pH. I would use a broad fork, sinking the tines in, then lifting the soil in place
without turning it over to preserve the soil structure as is. This is less important if the soil is just lifeless dirt.
Ask if soil tests have been done, or if they have someone on municipal staff doing that. You never know. If all else fails, you might want to have it done yourself, but you can also look at what's growing in the plots, and that can sometimes give you an idea of what's going on there.
In my city, urban arborists will gladly drop a truckload of wood chips to you for free, as long as you can take enough of them. If the same can be said in your situation, I would jump on that as soon as possible.
It is a really intensive step, but charging your plots with compost extract is probably the single biggest step you can take to rapidly increase soil life and productivity. Bryant Redhawk has a number of really great threads on the subject of soil and including great information about how to make things like biodynamic-style preparations, sub-surface compost extract injectors, and compost extracts, as well as everything else you'd expect. I have linked to the list of threads below.
https://permies.com/wiki/77424/List-Bryant-RedHawk-Epic-Soil
What do you want to accomplish?
I mean, if you started up a vermicomposting plot and gathered organic wastes from reliable sources, you could, for instance, sell vermicomposting worms or quantities of their castings. You would need to do the legwork, as with any self-employment, but that's a return you can realise before the first season ends on the investment of your time and some labour involving spoiled organics and the wrigglers.
If you had an excess of woodchips, some reclaimed pallets to box in the shadiest plot, a tarp, and some spoiled mushrooms of a kind that would take to the specific type of wood chips, you could make a mushroom slurry with compost extract and a blender, inoculate the bin of woodchips, and harvest mushrooms, probably within the first season. It's entirely likely that, by the end of the season, you could be selling either mushroom compost or inoculated wood chip mushroom starters, both viable streams of income.
If your aspirations are to grow enough food for your household, and you want to be able to set up the drip irrigation and plant support infrastructure, and visit on evenings and weekends, to harvest when it's done, you can do that. I would think about companion planting in guilds. The Three Sisters are an example you've probably come across, an aboriginal technique of growing dried crops that involved corn, beans, and squash, where beans fixed nitrogen for corn, whose stalks supported the climbing bean, and squash, who's leaves shaded the soil (I believe there are other sisters added regionally for things like attracting pollinators, too). Adequate spacing and watering can make this technique work for wet-harvested crops in an intensive gardening setting (I have done it).
My favourite guild is actually my tomato guild. I grow many different kinds of heirloom tomato, but my favourite is Watermelon Beefsteak. I interplant with basil and use oregano as groundcover.
I prefer purple basil because I get reliably better yields, even over other basils. I think it's because the red in the purple pigmentation reflects the red spectrum light in the sunlight, increasing the percentage of red spectrum light in the tomatoes' diet, and red light is known to be advantageous in the flowering and fruiting stage.
Additionally, although I don't have a link to the study handy, it has been shown that basil grown within 10 inches of a tomato plant can increase that plant's tomato production by twenty percent.
I brought up tomatoes because they are an example of a higher-value produce that can be grown in quantity on the garden scale. You could grow potatoes and onions (and if you want to, do so, by all means) but if your motivation is primarily financial, you might want to look to higher-value choices.
If you are looking to make money, my bet would be on the vermicomposting route. Worms are probably the only livestock you are going to be able to keep there, but that's an inroad into deriving cashflow from the city's organic waste stream, converting rotting produce into worms and worm castings, and into that ROI you mentioned.
Keep us posted, and good luck.
-CK