@Bryce Preston, I am seeing in your log where the update does happen and the new .402 Windows Update client is installed. About 2 minutes later, the system reboots and then shows the old version again.
I will show the errors I see so you can research them but do you have quite a bit of free space on your drive? You can look this one up but the sites seem to suggest cleaning the drive and removing stuff which to me, it a way of freeing up space on the drive.
Got error querying the post-reboot status for session 30662016_1293861139: 0x80010108
Another error I am seeing is 0xf0922 which I cannot find but references are made to .Net but it could just be the same type of error during install as Windows update.
I am not an expert at reading these logs, so keep that in mind. If you had your Setupact.log from the Windows\Panther.img hidden folder you might be able to pin it down using the times of the problems in the Update log. Such 18:05 on the 26th.
If they are going to release the public build upgrade on Monday, it might take care of some problems .. I just can't say.