Jim Fry wrote:"...and getting these suckers ripped out shouldn't take too long."
When you pull out plants in the winter you usually have to get every root also, or the plant can/will start anew come Spring. My suggestion in your case, because of the timing of your "weed" clearing, keep a close eye come Spring for new shoots. Then keep whacking the new leaves off until the plant runs out of energy to grow again.
Chinese privet will definitely come back from every little root fragment, and seeds will keep germinating in the vicinity for years. We had one in our yard when we bought our house in 2020, which I removed in spring 2021, digging up the stump and trying to get every single root. The next year I still had to pull dozens of sprouts from roots and hundreds of seedlings. Then a few roots still had enough energy to try again this year, and at least a dozen more seedlings this year too. I'm hoping next year the battle will be won, other than when birds occasionally deposit them from elsewhere (along with the Himalayan blackberries they bring every year).