I admire you for not wanting to use chemicals but you know, some of the time they work out to be the best choice if applied carefully.
I had an applicators license for most environmentally challenging things years ago and two products I used for complete restarts were:
2. Calcium Cyanimide
Vapam gets sprayed on and then everything gets covered with tarps and people are paid to watch it all for a couple of days. Lift the tarps off and nice, clean, soil to start over with.
Calcium Cyanimide was applied as a granulated powder as I remember. When it hit the soil, it created cyanide and killed everything within the soil. Weeds, bugs, fungus, etc. The cyanide evaporated leaving calcium behind in a week or so as I remember. You had to keep people, pets, kids and so forth of the application but you did not have to tarp it.
California was aggressive about EPA type controls early on so it was a challenge to use these sorts of things. For all I know, you may not be able to anymore.
Harsh as they sound? It sure beats running around with gallons of roundup with residuals that never convert or leave the environment?