SSL Offloading and Backend pool https

That is correct, adding the names including the CN into the subject alternative names section should correct your issue with the SSL certificate. That error you're receiving in your browser is because the browser has decided it's malformed information or some other information that could cause issues so it sends you that error instead. Using SSL over a non-standard port shouldn't cause any issues as long as you aren't using a port that is used by some other well known application. You should be able to do the following in your browser and it will be fine.

https://www.example.com:8444/

Sending this to the pool members on 8444 shouldn't cause an issue either. The only thing that I can see causing a problem is if you have an HTTP profile configured when you aren't terminating SSL on the LTM. If you are just listening on 8444 and sending traffic to a pool that has each member configured as 8444 or any other port it will work. Just make sure you have the FQDN you are using in the CN or subject alternative name and it shouldn't produce an error. Because of new rules with SSL certificates you need to make sure the FQDN in the CN also exists in the subject alternative name as well as all other names.