Hi, I need a bit more of information to be of any help. Here some question:
delivery speed: what value did you set?
email list: is your message listed in sending status? and what about the number of email sent/total email expected to be sent?
the “delivery engine next run” you can see on top of the plugin pages, is reporting big negative numbers?
did you set up a cron cal as indicated on delivery engine page (start from newsletter official page) to be sure the cron system of WordPress is running smoothly?
delivery speed set to 10000 per hour
the mail status is still sending 916/19112
the delivery engine next run is reporting -14701 seconds
I set up a cron cal from setcronjob.com
That means it is not triggered correctly. About your configuration on cronjob? On diagnostic panel, enable the logs at debug level, then on wp-content/logs/newsletter/main-xxxxxxx.txt there is a file which should report if the cron is called every five minutes.
Ask them to setup a 5 minutes cron that calls your wp-cron.php. More indication on my page dedicated to delivery engine, start from https://www.thenewsletterplugin.com/plugins/newsletter. A technician must be able to setup this kind of simple system administrative procedures.