IIRC, the User Template folder in /System/Library is exempt from SIP. I don't believe you need to disable SIP to modify this specific location.
If you're able to access Desktop and Downloads by navigating to them, but unable to access them directly, I suspect you're looking at two locations. Possibly, you have a symlink in place of an actual folder or maybe you've replace a folder with a file with the same name.
What do you see in Terminal if you list the contents of the User Template? I see:
sudo ls -hal /System/Library/User Template/English.lproj
total 0
drwxr-xr-x 9 root wheel 306B Aug 22 2015 .
drwx------ 37 root wheel 1.2K Sep 17 2015 ..
-rw------- 1 root wheel 3B Jul 24 2007 .CFUserTextEncoding
drwx------+ 3 root wheel 102B Jul 8 2015 Desktop
drwx------+ 20 root wheel 680B Jul 8 2015 Library
drwx------+ 3 root wheel 102B Jul 8 2015 Movies
drwx------+ 3 root wheel 102B Jul 8 2015 Music
drwx------+ 3 root wheel 102B Jul 8 2015 Pictures
drwxr-xr-x+ 4 root wheel 136B Jul 8 2015 Public
sudo ls -hal /System/Library/User Template/Non_localized
total 0
drwxr-xr-x 5 root wheel 170B Sep 17 2015 .
drwx------ 37 root wheel 1.2K Sep 17 2015 ..
drwx------+ 3 root wheel 102B Jul 8 2015 Documents
drwx------+ 3 root wheel 102B Jul 8 2015 Downloads
drwx------@ 9 root wheel 306B Jul 8 2015 Library
@preyman wrote:
I build a monolithic image each summer for deployment for the Fall and Spring semester.
Um...monolithic image?

Good Morning Preyman,
I wouldn't panic yet; I used to do the same thing with user templates until 10.11 came into town. My guess is your talking about your Dock icons and Finder links not pointing to the right folders? They have probably literally linked to your created Template User Desktop and Documents folder you copied to the English.lprog folder.
Due to this, I adopted Dockutil to set Docks in 10.11 and will for all future releases for as long as I can. There is another tool for Finder as well, I don't use it but I've heard it works well too.
Unfortunately, it sounds like you have a tight schedule. You could look into building a package with Dockutil that installs on startup along with a policy that will run a Dockutil script on login for each user. You can set the policy to run once per user per computer.
Another option would be if you could get a working Dock and Finder plist, you could have them copied to the User Template on startup. Or build a package with FUT/FET set that installs them to the Users preferences folder. There are also options to set the Dock through policy and configuration profiles.
I'm sure more people will share their expertise with you. Check this link as well; there may be some ideas in there to help you through this as well.
https://jamfnation.jamfsoftware.com/discussion.html?id=18357