clearing invasive weeds without the bad stuff

I have wooded areas in my yard where the ground is covered with virginia creeper, cherry laurel, privet, redbud seedlings, and poison ivy.

What is the best way to remove the invasive stuff? I'm hoping to fill with perennials that we can enjoy. I refuse to use the mainstream sprays.

I have already tried digging the weeds out by hand and it's not sustainable with my available time and energy. Is there something that would help the process go faster than hand-digging but is a better alternative to the chemicals I'm trying to avoid?

If there's already a forum with suggestions for this, feel free to just leave me a link there.

Thanks!

You can rent a couple goats to eat the weeds, followed by a couple pigs to root everything up, and now you have a fresh start for whatever you want, and well fertilized.

The farmer that rents the animals would most likely have portable electric fence to contain them.

Since you have all that nice mulch, you can use that afterwards to suppress the weeds and control erosion, and now you have a potential mushroom haven!

Tough question. I don't know the others, but Virginia Creeper thrives in Zone 3 and once it's established it's mighty tough stuff. I imagine that chopping it to ground level every few days will eventually starve it, but you really have to want it. And then when you think it's dead it will pop up later. Think of this as a multi-year project. My 2c.