You want to try some river crossings? Try the Verde just down from the Childs power station. You can get there from the East side by coming down from Strawberry or Camp Verde and you can get there from the West side by going back into the Bloody basin, and down around Red Creek. There is another river crossing at Sheeps Crossing just up a little bit from Horseshoe lake (normally empty), up northwest of the Cave Creek area. After crossing there, you come back out just south of the Bartlett dam area. Only cross during low flow and even then good luck as only the heartiest seem to make it. Still, that does not stop lots from trying... just make sure you have a long rope and somebody with you to drag you back out when things go wrong.
Mud????? Follow the rain storms. I've never had a problem finding mud when the conditions are right. Good luck finding any around Phoenix as the monsoon season this year totally stinks. Head to Tucson and go out Reddington pass. It seems they have been getting rain every other night and are 2 inches above average so far this year. You could also try box canyon just north of Wickenburg which is probably pretty wet about now but stay out of there if there have been any storms upstream - can you say FLASHFLOOD!!!???? At it's narrowest, it is not much wider than a vehicle and last time I was out there, there was a big hole right in the middle of the narrow part. It's a sandy bottom but seems solid as long as you keep moving.
There is also a big ORV area past Cave Creek southeast of the junction where you turn off to go to Bartlett lake. Wait for some rain and then try out there but watch out for the motorcyclists. It kind of sounds like you may be better off waiting for a cloudburst and then playing around in the big empty dirt lots behind some of these home improvement stores.