Good news, I found a solution to this frustrating issue!
The error I kept getting was 'Invalid Authorization Code', even though I copied and pasted it exactly.
The way I resolved it was to contact the current registrar via their support chat and simply have them reset the Registry Key / Transfer Auth Code. It took 5 mins to complete and the new code worked with the Squarespace transfer process. No need to contact SqSp support.
You're welcome 🙂