I've had the same issue. I finally resolved it by going into PayPal and deleting Squarespace as a 3rd party processor. Then I came back to Squarespace and started the process from the beginning once again. I accepted every option provided during the set-up process, PayPal's and Squarespace's. It finally works. Time for a drink.
By the way, Squarespace Customer Support just gave me a bunch of links to guides that I've already read. I resolved this on my own.