So, last Tuesday, the tree guys removed it all while I was at work. Apparently it only took a couple of hours and they left no damage and no debris. They did, however, leave the stumps, but those should be ground out shortly.
The next phase of the project includes reseeding certain areas with grass seed, planting new plants (of the placement and type I am unaware, but trust my wife’s judgment entirely), and finishing with mulch and such. That work should commence next week.
Right now though, I’m just looking at some stumps and bare dirt around the house, but I can already see that it’s going to look MUCH improved. The fact that it’s going to be less work, less worry, and give us more usable yard is even better.