Use AppleScript to send all emails in a folder at a certain time
This is not necessarily meant to be a complete answer and is too much as a comment. Because the Mail AppleScript Dictionary lacks some verbs, e.g. send again, one therefore needs to workaround any shortcomings.

The code below could be incorporated into your script. It uses System Events to manipulate menu commands to send composed messages from the designated mailbox.

Example Code:

tell application "Mail"
    activate
    repeat with theMessage in (every message of (mailbox "9AM"))
        open theMessage
        delay 1
        tell application "System Events" to click menu item "Send Again" of menu "Message" of menu bar 1 of process "Mail"
        delay 1
        tell application "System Events" to click menu item "Send" of menu "Message" of menu bar 1 of process "Mail"
        delay 1
    end repeat
end tell


What this does is automate the tasks that one could/would do manually to achieve the same results, sending the unsent saved messages from a given mailbox.

What this doesn't do is, if the mailbox is other then Drafts, remove the messages from the target mailbox and additional coding will be required.

Notes:

The problem with automating a series of manual tasks in this manner, aka. UI programming, is if at the designated time the script runs and you are doing something else and it take focus away from Mail then the script will not be able to properly complete.  This is because if the Mail menu is not visible then the calls being made by System Events cannot be completed.

The value of the delay command may need to be adjusted, e.g. delay 1.25, if required or whatever value works on your system.  Slower systems need higher delay values.

Obviously if the target mailbox is Drafts keep in mind that unless you code accordingly all messages in the target mailbox will be sent and therefore using e.g. "9AM" allows keeping drafts that aren't ready to send from being sent. The disadvantage of other then using Drafts is requiring additional coding to remove the messages that have now been sent via Send Again > Send in this manner.