Your scenario is exactly i’m using for years. And in addition to the suggestions you already have like to share my solution.
I use a less known service: batched SMTP. Not all Domain/E-mail hosting providers have this option and had to switch to one which does.
BTW You are better of to make a new topic in the future if you want to discus/support a specific scenario off your situation . @alefattorini or other moderator is it a good idea to split this off?