I finally had a chance last week to reach out the QuickBooks Desktop Support team, as directed above. The support person I spoke to was eager to help but was ultimately unable to provide me with any IP addresses or FQDNs that QuickBooks needs to connect to in order to validate its license. She said she would elevate my issue, but a few days later responded by email with this:

“I apologize about the delayed response but have not been able to get the IP address in question for this issue. I will continue to research and if I am able to find one will reach out again."

Joestar summarized the problem the best above in a few sentences.

If anyone else in the community is ever able to discover the IPs of the servers QuickBooks Desktop is trying to communicate to in order to validate its license, please post it here if you can. I’ve been investigating this myself with the help of WireShark, and so far, it looks like QuickBooks Desktop is reaching out to a number or Amazon datacenters, so I assume Intuit is hosting their license servers with Amazon cloud. There’s still too many Amazon IPs connection found for me to determine which specific one is for license validation, or if there are many needed to add as exceptions on our firewall.

Thanks.