I'm not sure where the final fix came from, or if it was a series of different things, but it appears to be up to date now.
I installed about 30 of the updates manually, then before I went to lunch I kicked off the Windows Update. It found another 30 or so updates and installed them with no issues. After a reboot it says that I am now up to date. I really do appreciate all of your help with this, because there is no way I would have figured this out by going through the logs.