Quick update. I uninstalled Brave completely on the new system. Reinstalled it and closed it as soon as it launched as part of the installer. Then I copied the same files over from C:\Users[Your User Name]\AppData\Local\BraveSoftware\Brave-Browser\User Data\Default and it worked this time!
I have my 248 BAT back! Woohoo! Thanks for the reply ShineWhine…it prompted me to try it again with a clean install.