How do you accomplish 5 and 6 atomically? I assume it involves proof of payment, the hash preimage from the lightning invoice.
This step is not atomic, you trust the mint to give you ecash. I don't think you can do it atomically.
Pay ln invoice to receive ecash. Can that be made atomic with PTLCs? Instead of hash preimage buy a private key as the proof of payment. If the mint pre-commits to the (blind) signature nonce R (similar to DLCs) the lightning invoice could use s*G as the point to pay to. The payer would verify that this point is hash(R,msg)*P+R to know that the proof of payment will actually be the expected ecash (signature)