Okay, you’re not digging, but are you mulching?
Wild hearing about June 1st being too hot to garden in your climate, as here in Quebec, on June 3rd it’s still too cold for most plants to go into the ground…
It sounds like, in your climate for what you want to do, you’ll have 10x better success if you were to apply deep mulch. I’m talking 8–10" deep. It’s hard to tell from your photos the status of your mulch (but it looks very scant). Check out the 24 minute Ruth Stout video on YouTube (with subtitles, I think). I’ve had the best results with haphazard combinations of straw and wood chips. I don’t know the square footage of your garden, but from the photos and descriptions, I would think you’ll need at least two full-size rectangular straw bales, and probably two or three good wheelbarrow size loads of wood chips.
I think the thing about Fukuoka’s system is that he’s talking about growing not just rice but cover cropping — which means he’s throwing massive quantities of organic matter on top of his soil.
I’ve had this same thing happen with nearly the same corn variety. In addition to the heat, and probably a lack of water, I would strongly wager that the small size and quick (scant) fruiting is a direct result of your having not fertilized. Corn is very very demanding. In fact, so are all the plants you mention here. I would strongly recommend getting your hands on some Acti-Sol or something similar (a pelleted chicken manure product).
I also worry that your melons will ever only grow to fist size or smaller. I don’t know much about growing in hot climates, but I wonder if you could extend your growing season by throwing up a shade net — either one you leave in place, or put up between say 10am and 4pm.
Also, just because you’re practicing no-dig doesn’t mean you can’t or shouldn’t try to fork and deeply aerate your soil — next time do it before laying down your layer of compost (which will add more for you than just regular garden soil).
Just my thoughts. You can send me Bitcoins if you find it valuable! ;)