what is the correct sequence to amend a return if I havent filed my state return yet?

Here's my situation

- just efiled my 2022 federal after getting an extension.

- discovered errors in my 2021 returns while preparing the state return

Now I need to amend my federal and state 2021 returns.  Federal has to be mailed, state can be efiled (I think) amendments.  When you efile, it takes about a month to get processed, when you mail it takes about 3 months.

 

Here's my thinking

1.  Mail 2021 amended federal return now.

2.  Efile amended 2021 state return now.

3.  Wait a month, then mail 2022 state return before Oct 15 deadline.

4.  Wait 3 months until Dec 2023 and efile 2022 federal return amendment.

 

Is this a good sequence to allow for processing of returns?