Most of that stuff comes back from itty bitty pieces of root and it is soooo hard to get every little piece. I think that your best best is to paint the leaves of the plants with something like Ortho's Bush-B-Gon. It is taken down into the root and kills it. Some things like the honeysuckle will take time as you have to keep treating the new sprouts. Do it when they are young. Don't let them get a head start.
PB

Hi PB!

I've been using Brush-b-Gone and similar products by the gallon. It still doesn't prevent some other opportunist from fill the void. And it really doesn't get every thing. I've got a Hudson sprayer that I spray while my husband runs around covering the native shrubs.

Brush b gone has little or no effect on the smilax or dewberry over the long term.

I think I've talked my husband into tilling it all under, but that still means we'll have to plant something in there or some undesireable will still take over.

Clarenancy

Over the years I have helped many customers regain control of large, overgrown land parcels. Do not till the land! Big mistake. The bottom line is that until the trees grow and cast deep shade it is necessary to brush cut the land three times during the growing season. More often, if you wish. A brush cutter will turn that land into a a park with minimal effort. Google "walk behind brush cutters" for an idea of what is available and easiest to use for your situation. The brush cutter will chew up into fine mulch everything it passes over. It's good for the land. Also, when removing vines on trees, cut the vine 12" above the ground and then paint the freshly cut stump with full strength brush killer. If it starts to sprout again, make a new cut in the trunk and repaint with brush killer.

Hey Nandina!
Thanks for the advice. It's encouraging.

I saw a brush cutter last fall in the rental department of Home Depot and wondered how they worked. But I'd forgotten about seeing them until you mentioned it.

I do paint the stumps and vines for the most part. I must admit that some of the vines are more difficult to paint than others. And, of course, some are tougher than others.

I'm going to get my hubby to research this brush cutter. I'm sure it's not easy to handle but it can't be harder than what we've been doing.

Clarenancy

Ditto on Nandina's advice. I've done it as well and after cleaning up the ground trash I was actually able to mow with a riding mower. Never mind what I was mowing was just weeds - they were just the tender shoots and keeping it mowed short allowed some grasses to take over.