Toil, I never doubt for a second that if AS suddenly comes across a half acre, she might try rice.
I hope you come across some land yourself. Still it seems you are keeping in the realm with the 'scope, and learning time has great values as well...
Daikon has become a darling of the permaculture movement not simply because they reseed easily, but because large root vegetables have a mechanical effect on soil as well as the chemical soil building we talk about often... these crops wedge down into the soil, breaking it up and moving towards sub soil, wherer minerals often depleted in upper layers are more abundant. This is Nature building soil friability; think of it as slow motion plowing (without the work or the soil damage).
There is a level of intervention in cutting back those weeds around the melons or planting out sets, there is a level of intervention in composting, there is a level of intervention in weeding, there is a level of intervention in using herbicides. I think the important thing here is to match a level of intervention you feel comfortable with to a level of intervention that does the least amount of harm to the environment, as that is what is best for the plant in the long term.
I think how we treat weeds usually is less beneficial than F-san's kama to soil biologies, and therefore is deletorious to plant health in the long run. I am switching up strategies and I do not expect this year to be what I get in the long run; I think every year will bring increasing returns. There is a slightly delayed gratification to organics, or gardening naturally, that puts many off of this approach. But the successes come more easily with time; the tomatoes this year are more prolific, disesase free and, most importantly, tastier than ever. My soil is sweetening and strengthening, the worms are getting more prolific and vigourous. The garden ran on auto-pilot this year due to mass distractions, and for the most part it has been successes. Natural gardening is not only possible, it is sustainable, and with less effort. It only takes a change of mind to make the change in the garden...