Replying to my own topic - the problem was indeed that my account was in a messed up state. I hadn't noticed the little red (1) over the bell icon at the top right of the main site. What it was trying to tell me with its teeny tiny little red (1) was "OMG YOUR ACCOUNT HAS BEEN LOCKED DOWN!!! YOU CAN'T SEND MONEY UNTIL YOU SEND US PROOF OF IDENTITY!!! AGAIN!!!".
Hot tip: if you log out of paypal and try your purchase again, you can enter your credit card to make a paypal payment directly without logging in or signing up (even if your credit card is on a locked down account).