Sorry, I figured it out.
The solution is that you can specify multiple groups using the SDDL (which I didn't know what it was, but it is short-hand for some authority settings plus a SID).
So I did a netsh http add urlacl url=http://+:47001/wsman/ sddl="D:(A;;GX;;;[redacted])(A;;GX;;;[redacted])"
And it finally restored the settings to what they were before. I should note you have to get that above syntax exactly right in order for it to accept it. Also there are some PowerShell commands you can use to translate a user account (like the ones above) to a SID if you need them.