As far as the crickets go, maybe you could put the container on top of a stool or table or something and put a ring of Vaseline around the legs so that if the ants try to go up them they get stuck?
Letting the frogs go without soil in the tank would work, but you'd have to clean up the bottom of the tank when they poop. You could put down paper towels to make cleanup easier. I wouldn't keep the frogs in the small tank very long, but it should be fine just long enough to clean out the big tank.
As far as letting the frogs go, I wouldn't do it in the middle of a drought unless I could put them near a body of water. Personally I'd think their hunting skills would still be fine. Some people might disagree. The frogs are probably less scared of people than they should be but I understand wild Australian Green Tree frogs are pretty docile already so...?