Around 7:30 on Friday I "got up" for good. I ate a quick breakfast and got on grubby clothes once again. I cleaned out he rest of the pit except for maybe 1/2" of sand. The plumber never called beforehand, so I couldn't tell them I didn't need the vac truck. Thankfully they were nice enough to not charge for it when they got here.
Installing the pump took a couple of hours. We used the small pump a few times during setup. I got a little nervous when it began to back up during the longest stretch, but pretty much as it was cresting the top of the drain, we turned on the pump for the first time. It took less than 15 seconds to drain the pit.
After that they had to rig the drain pipe outside, which did not take too long. The first 2 runs just sprayed it out onto the back grass. They set up PVC pipes to route the water about 10 feet from the back of the house. Then they cleaned up and tallied up the bill. While that was going on I learned about yet another oddity of our house: The 3-prong plug in the ceiling of the basement is not actually hard-wired into the panel. It runs to another 2-prong plug in another part of the ceiling. So not only are the plugs piggy-backed, but the 3-prong outlet is not grounded. I should also point out that it is 3 feet from the electrical panel while the one that feeds it is about 8 feet away. OMFG!
The total bill for the two days ended up being a bit over a grand. That is a lot of money, but could have been worse, plus I saved myself $750 by digging out the sump pit myself. The pump runs great. It is a little noisy, but it is tolerable. Plus once the water outside goes away, it shouldn't run as often. It might run almost never. We never had a problem before and we didn't have any pump. I might raise the pump a little in the pit. I'm afraid that right now it is a little below the natural water line. If I put a couple of bricks underneath it, it should run less often. That will require cutting the PVC, but that is easy enough to do.
Skipping forward to today, we bought another 10 foot piece of PVC to extend the existing one to get the water a little further from the house. Eventually I will reroute the outside setup so that it runs along the fence line and empties closer to the trees by the fountain.
Part 3, theories and aftermath will come later. I don't feel like writing them up tonight.