I recently changed the configuration of the Mailpoet plugin on wordpress for sending our newsletter. This should solve the issue reported during this meeting.
First, I created an account on Mailpoet's website. We must use one service plan per site. In our case, we have 3 sites (fr, en, nl).
I could subscribe to two free plans max, which are limited to 2000 subscribers each.
For the English site, we have about 1500 subscribers, while for the Dutch site, we have about 400 subscribers, and for the French site, we have about 300 subscribers.
So, I changed the configuration for the English and Dutch site. Sending a newsletter from those sites should be almost instant :)
For the French website, we still send mails through infomaniak, in SMTP. This will be slow, but as we won't reach the 1440 mails/day limit, I increased the amount of mails sent (100 mails/5 minutes, instead of 5 mails/5 minutes).