I don't know why I didn't get a notification of your reply until this morning. So, sorry for the delayed response.
I've tried several reboots, and have downloaded the updates both from the sys tray and the shutdown menu multiple times. And yet, when the machine reboots, the updates show up again. As I mentioned before, it seems to be stuck on downloading the August update of the Malicious Software Removal tool. When I go to the MS updates site, it lists the tool as being the only update I need to install, yet the file to download is listed as being "0 bytes" in size. According to that site, I've downloaded this update successfully every single day since the patch was released. Sometimes multiple times in one day.
Typically when I install the update, the status screen shows the file being downloaded and installed, followed by a message saying "installed successful." Then the install shield in my sys tray disappears, as well as the one in my shut-down menu. However, around 30 seconds later the shield icon reappears in both locations asking to download and install the exact same file again.
Something strange is going on here. Originally I thought some piece of malware was blocking the updates from installing, which is why I came here to this forum for help. But now I'm not so sure that this is the case. Not for this particular issue, at least.
--Ryodin