Royally messed up my Windows Server 2008 R2

Solution 1:

1. Disk Cleanup can take 1 to 4 hours. It's NORMAL to sit at 100% Configuring updates after rebooting. If you can't wait that long, don't run Disk Cleanup.
2. You should always have a current backup image of your server so you can easily recover if necessary. We use Macrium Reflect Server.

Solution 2:

My guess is I will need to delete the boot folder in the "System Reserved" partition [...]

I hereby confirm, that this is NOT the way to do it. The reserved partition is there to boot (NTLDR) from and that's good; don't worry about the disk labels, the Windows kernel knows how to handle this (usually the boot partition does not get any drive letters, so you can savely delete THE LETTER).

[...] but got stuck [...]

I have seen a lot of "stuck" machines that were not really stuck. Just give it (a lot) more time - I have waited up to 20 hours for a (slow) machine to come up again.