If I understand it properly, the mint signs an encrypted message, and the signature survives decryption, sorta like if an envelop had carbon copy paper inside, a signature on the outside survives the destruction of the envelope (that is, decryption).

So, the ballot tokens are minted, encrypted with the voter's key, sent to the voter, decrypted and selected by the voter, and broadcasted to the verifiers. The selected tokens are verified with the booth's public key and are not traceable to the voter.

To make it more secure, a voter would send a separate verifiable message authorizing having voted, which is weighed against the total count to keep the booth itself from just broadcasting fraudulent extra votes.

I think I need to draw a diagram.

PS: This could be multi-layered, too, like onion routing. A Teller service could request tokens minted on behalf of a third party from the main mint and store them securely until they need to be issued. The teller makes a withdrawal send to the third party asynchronously.