I'm afraid I don't have any good news for you. You might try applying crushed activated carbon from an aquarium supply place. Carbon absorbs chlorine in water, but you're really in the vapor stage at this point. It could be that air and time are all that's left to dissipate the chlorine. It will go away, but not before the damage is done.
Actually the damage is already done. Besides the chlorine you have the flooding that kills off the fungi. Fungi are all aerobic, so they're history if you had standing water for any length of time. The only similar situation I can think of would be if someone spilled a chemical fungicide on your lawn. Maybe a drench of pure alcohol would be worse.
I think your neighbor should be more than sorry. He should offer to help you repair the damage. When he sees the yellow grass turn to brown (dead), he should offer to at least split the cost of repairs for you. You might need sod, shrubs, compost, organic fertilizer, maybe a tree, and delivery for all that. The tree might be okay because of the deep roots, but grass and shrubs are less likely to make it.
The only possible saving grace is that the guy was typical of some home pool owners and never kept enough chlorine in the water to begin with. Was the pool always bright blue or was it sometimes covered with green algae? If he had algae, then you might have actually gotten out of this unscathed except for the fungi thing. Chlorine is hard to keep enough of in a pool, so unless the guy was extremely diligent, you might get off with just the flooding problems.
What I would do is wait for the ground to dry out a bit. What I'm going to suggest is to put compost on as a semi mulch but you don't want to trap chlorine under the mulch. So wait for it to dry some. IF the sod looks green after 3 days, you might be okay. But still, apply compost at a rate of 1 cubic yard per 1,000 square feet to reestablish your microbial population. Then apply corn meal at a rate of 10 pounds per 1,000 square feet to feed the new microbes. I don't think you need to bother with greensand or lavasand. Molasses, seaweed, Medina soil conditioner, and Medina Hasta-Gro are all products I would consider, but don't expect a miracle. If you want to speed up the process, you can reapply the compost and corn meal in a month.
If the grass is alive, seemingly thriving, but still very yellow after a month, then apply greensand at 40 pounds per 1,000 square feet. Give it 3 weeks to turn the grass green again.
Your tomatoes should be fine to eat.