Yard takeover

Well I goofed. Tried to clean up the back corners of my lot. I knew enough to recognize some poison ivy and small mulberry bushes. Turns out the poison ivy had dozens of 1"+ vines climbing a half a dozen 60ft tall trees, along with a whole network that tunnels along the fenceline for 20+ yards.

Even worse, I learned that the trees that the poison ivy was killing are honey locust. Now that entire corner of my yard is booming with rapidly growing honey locust plants. Apparently these things are very reactive to any physical manipulation.

The other side of the yard cleaned up much nicer, but already has sprouts of poison sumac and poison ivy springing up.

Any suggestions to reclaiming this mess?