It depends on the motor. I have seen Pro Wedges work well on smaller motors. They don't work worth a shit on our big DMs.
And yes, the cut Ambush hook harder than 501s.
Yes, I have run tons of dirt tires. The Ambush hook much harder than Turf Tamers. My tires are 23x11x12. Unless you have a big motor you won't be able to turn them very easily.
You will likely want the 22x10x9.
Terrain Traks are a paddle tire. There's no way they are going to hook harder than a cut Ambush on hard packed dirt.