Thanks, hero! You're my hero.
However, I still ended up hosing my system, believe it or not. When I went to copy the profile, I noticed there were both C:\Users\Default and C:\Users\Default Users folders in there. So I tried looking up what the difference was and the best I could get was they were there for backwards compatibility.
(As a side note, I did finally come across directions online for modifying the Default profile,
https://forums.microsoft.com/TechNet/ShowPost.aspx?PostID=1452752&SiteID=17)
So I overwrote the \Default profile and tested it, and it seemed to work, but I still got things like the "Gadget" bar coming up, some Lenovo registration prompts, and some other things I had tried to disable in the template profile that did not copy over, so I went back and tried overwriting the "C:\Default User" folder. Big mistake! After that, any new user I tried logging in as who did not already have a profile, I got an error message about the profile manager could not logon and the logon failed. I tried to restore the C:\Users\Default User to a previous version within the folder properties (using Shadow Copy snapshots), but kept getting an access denied message, and then all the previous versions disappeared after the 2nd attempt. I tried a System Restore to the previous day and that fixed the logon problem, but then I got odd \Default User(147) \Default(136) folders and the system does not work right; network connections keep dropping, some previous programs I installed won't run and I can't seem to reinstall them, etc.
So I'm just going to wipe it and start from scratch as I'd rather have a healthy system as a base template to start with. But this time I'll only overwrite the \Default folder and leave the rest alone.
Assume that I already did an Internet search.