Studying different fields, I tend to think that root knot nematodes do not like heavy soil, but flourish in sandy soils. So, without intending to, you have already begun the battle by adding so much organic matter onto your sandy garden. It is unfortunate that baking the soil will also kill some of the good flora and fauna. Perhaps you can convince the grandchildren to rake away the organic stuff, then bake the sand. (Finding good nematodes seems a lot easier.)
Wish I could be more helpful. I have been blessed with super heavy soil with serious clay hard-pan...So not much practice whipping root knots these days.
I'll probably stick with solarization.
I'll add good nematodes. And I'll grow tomatoes in pots next year, and maybe the year after.
I'm not sure I'll be here in 3 years, so I'm not going for the slow methods.
I have innoculant for the soil to re-introduce good microbes. I'll have that checked for nematodes. I may have grown some last year with the manure tea.
I'll fix it, but it does make me wish I had a WWII flame thrower.
I'm not subtle.
/johnny