Those look like some kind of shrub seedlings, not annual or perennial weeds. If so, a rototiller probably wouldn't work to dislodge them. Also, depending on what type of shrub it is, rototilling could actually help the plants get thicker with suckers arising from chopped up roots.
I'd use my friend's time to manually dig as many as possible, getting as much of the root systems as possible.
If it is some type of annual or perennial weed it becomes a matter of season long control next year, not allowing anything to go to seed and constantly destroying anything that pops up.
Welcome to home ownership! Like your cat (panther?).
hortster

Was this property vacant for a while?

Please call "call before you dig" before you dig anywhere a first time. Ask to have the whole property marked, all utilities, then take pics so you don't forget, they won't come out every 5 minutes. Take notes which color is which utility. If you do and something is damaged that is not marked, it's not your responsibility. If you don't call first, any damage is your responsibility.

Check the cable TV line again yourself. I've discovered them just laying in flower beds. Also, things are often NOT buried as deeply as they say they are.

I don't think tilling can remove stumps like that - but I've only watched that action.

Uncovering the bare earth all winter is not the greatest idea. You could have a lot of erosion when it rains and since that's a wet time, you'll have worse compaction. If you are able to put a layer of straw or leaves if you do any excavating, that would help a lot, as well as begin to restore the soil to its' natural balance and add some organic material to aid with the texture of the soil, and the fertility to a minor extent.

May be "shrubs" growing from roots of a removed tree.

As was suggested, you can dig out.

You can also use herbicide, but you'll have to wait until new growth occurs in the spring.
- Wait until the spouts grow and leaf out fully,
- cut them all to the ground, leaving only short stubs which you immediately paint with triclopyr on the cut surface.
-Repeat as needed. (Likely this will require several years.)

Any chance you are able to get a vehicle positioned to pull them out? Wrap a tow strap firmly around the crown and attach the other end to the back of a truck or 4-wheeler and then slow-and-steady just pull them out. (This is way funner than trying to dig them out!!!) Some roots will break off, and if it's a suckering type of shrub, they will send up shoots down the road. Those shoots will be young and weak though, and if you spray them with roundup as they emerge you should probably be able to get rid of them completely within a few seasons.

You'll know if this is a suckering plant if you pull up a clump, and it's connected to another clump.

He went into the corn...

I removed a large English Yew once.
I used a shovel to dig around the roots as low as I could go. I then cut as many roots and branches as possible with loppers.
For the last "step" I had to channel my inner cavewoman. I took a 6' long steel pipe and bashed the heck out of the remaining roots until they broke. Then I threaded the branches into the pipe and used it as a lever to tear the thing out of the ground. It was a very barbaric way to do it but it worked. It probably took 2 or 3 hours and a lot of muscle. But it was free and a better workout than crossfit.