I don't think there is a way you can do this reliably. As soon as you manually put focus on the invalid input, the screen reader is going to stop announcing your list of errors in the live region and announce the input you focused. You could put a delay on the focus to give the screen reader a chance to announce all of the errors in the live region, but then you'll be guessing how long that will take.

One common method for announcing a list of errors is to move focus to the list and make each error message a link to its input. You could also not move the focus at all and just add the errors to the live region. Also, creating a master list of errors is not required. You can just add the error messages to their inputs and put focus on the first invalid input. If you are going to do a master list then I would recommend you move focus to it and add links to the inputs.