The worm prods are used for gathering worms for fishing. They work great. You wet down the area and stick the prod in. Plug it into an extension cord and out come the worms. Wouldn't have believed it if I hadn't seen it. Will it get out the crayfish? Dunno. Worth a try. If it doesn't, you can at least go fishing.
Water softener pellets are basically salt. I use them here to melt ice with on my porch. They're bigger than rock salt or ice melter so they cut big holes, plus because they are bigger, there's usually some of them left at the bottom of the ice hole, which seems to help future build up. Will it get the crayfish out? Dunno. It worth a shot. The idea is to create a habitat for them that is a little less desireable so they will go elsewhere. I was hoping that raising the salt content might get them to move. I would expect damage to the lawn/trees to depend on how much salt you used. Lots of salt, kill everything, little salt probably not hurt much. They still brine and salt some roads around here in the winter, have for probably 50 years. Stuff still grows on the shoulders, so I thinks its probably going to take a lot of it to kill trees and grass. Still, if the tree is recently transpanted its probably pretty shocky right now and who knows what might happen.
I'd try the worm prod first. Look at tackle/bait/sporting goods shops. There may be one in Northern's catalog, I can't remember. I think the death was probably related to an electric fence. Wet ground, juice in the ground and in the fence. Probably not a good idea to touch both, you'd be making a direct connection from house wiring to house wiring. One of our resident electrical guys might be able to answer that one for you.
Just to throw out another idea. How about a windmill? One of those little ones that they sell for mole control. The vibration might be enough to make the little guys look for someone else's pasture.
SHF
PS the salt won't work if these crayfish are a saltwater variety. Still never saw them anywhere but at the bottom of the lake.