I couldn't delete the RemoteInstall folder
Interestingly enough, It was asking me for permission to delete the folder. I thought, no worries, I'll just take ownership of the folder and sub-folders then try again. No dice, though this time it was rather amusing since it was now saying that it needed permission from me to delete the folder!
It turns out I was on the right track for resolving this, but just didn't go far enough.
So, if you get "You need permission to perform this action ..." when trying to delete a folder tree, you can try the following:
1) Open an Elevated Command Prompt (Right-click Command -> Run As Administrator)
2) Run: takeown /f path/foldername
3) Run: icacls path/foldername
After running these commands against the RemoteInstall I was able to delete it and continue on to rebuilding WDS/PXE for my Distribution Point.