Anyone know if there's a way to copy over your WTF File/Folders/etc/ to the stress test client to transfer your UI settings?

Yes.

Simply go into WTF folder and then into Account folder.
If you have an account made pre WoTLK, then it will show your actual username into the account folder. Accounts made after WoTLK will have numbers instead like 115748671#1
Each folder in the Account folder is an account you logged into.

In order to copy settings from one account to another, or one realm to another or even one character to another.
All you need to do is rename the account name or rename the realm folder inside of the account folder of your choice.
You also want to rename the character folder inside the realm folder to the your new name (if you have decided to change your name)

If its all on the same account, you just need to rename the realm folders and character folder to the new realm and new character name.

I've done all this and unfortunately it didn't work. I imagine the beta client and current stress test are too different. Thank you for taking the time to reply though.

Thankfully I found a screenshot that had most of my bindings on screen so I'm saved.