Yes, your approach is good. You should keep them in separate envelopes, as you know. That said, a suggestion would be to keep them in those separate envelopes but send them together in one larger envelope. The same for the state.
Since each one affects the subsequent year, if you mail them completely separately (without waiting until the prior one is processed) they may question the tax reporting on those amended returns.
Also, I would suggest attaching a statement to each return explaining the situation to reduce or eliminate IRS correspondence.
Amending is done on Form 1040X. It
can take the IRS up to 12 weeks or longer to process them. If you are
due a larger refund than on your original return, your amended return should
only show the difference and you will receive a separate check for it. If
you owe money on your amended return, it will show only the new amount owed,
you will have to mail a check with the return.
How to Amend?
https://ttlc.intuit.com/replies/3288565
