I understand that you need a list of IPs or FQDNs from Intuit to add as exceptions to your gateway firewall, joestar. 

To get the list you need, let me direct you to the right person who can assist you. I suggest reaching out to our QuickBooks Desktop Support team, as they can provide you with the information you require and can even perform additional troubleshooting if necessary. 

Here's how to reach them:

1. Open QuickBooks.
2. Go to Help, then select QuickBooks Desktop Help/Contact Us.
3. Select Contact Us.
4. Give a brief description of your issue, then select Continue.
5. Sign in to your Intuit account and select Continue and then Continue with my account.
6. We'll email you a single use code. Enter your code and select Continue.
7. Select to chat with us or Have us call you.

To check for our Support hours, refer to this article: Contact QuickBooks Desktop support.

If you need to know the technical specifications required when using QuickBooks Desktop Enterprise, take a look at this information: QuickBooks Desktop Enterprise Specifications.

For more tips and resources, feel free to visit our website: Self-help articles.

Please let me know if you have more questions about IP or FQDN. I'm more than willing to assist. Take care.