Update again (apparently I need to try a few more things before I go and ask questions lol):
In case anyone else needs to know how to do this:
Everything you need to transfer for this is in the AppData folder, just in a few different places.
For Excalibur
C:\Users[YOUR USERNAME]\AppData\Roaming\Knights of the Editing Table
There is an "excalibur" folder in here with a handful of files. The one I had on my old computer had more files than the install on the new one, so I copied over everything from here.
C:\Users[YOUR USERNAME]\AppData\Roaming\SpellBook
There is a file in here called "knights_of_the_editing_table.excalibur", I don't know if you'll have this if you don't have Spellbook/Quiver installed, but this was the file with all of my hotkeys, presets, etc. for Excalibur. Once I moved this over, everything populated!
There's also other files in that folder if you have other plugins, for example my Arrow preset file was in there.
For Spellbook
C:\Users[YOUR USERNAME]\AppData\Roaming\knights.of.the.editing.table.SpellBook
This folder has your Spellbook profiles in it, just copy them over to the new computer and they should pop right up in Premiere!
Also, make sure you remove your old computer from the license manager here: https://license.knightsoftheeditingtable.com/account
And put your license key in on the new computer. For Quiver/Spellbook it has you do it right in the panel for Quiver, and for Excalibur you have to unsheathe it (ALT + Space) and then it'll ask you for it.
Hope this helps!