honestly your best option is to export that list; and then import it into an application that is designed for mass emailing.
I believe that attempting to turn an Access database into a mass emailing application is a round peg in a square space - - it just isn't a fit. Plus there are emailing applications out there already built and at a very reasonable price. Perhaps
even your own Outlook system.... so why reinvent the wheel....
Limit the role of the database to be the application that creates the correct set of emails; but then port the data over to an application that is made for emailing and has built in all the contingencies i.e. bounced back invalids, etc.
my 2 cents....