The issue isn't the network connectivity, it's the webserver itself. The server is located in San Antonio (with no edge caching!) and it's responding to pings just fine, so we know the DC is ok. When analyzing the traffic between my client and the server, I see that there's a huge gap of 15-20 seconds following my SSL connection before I get the first response from the server. This time to first byte is 100% an issue with the application that's acting as a webserver (it looks like litespeed) that's hanging for some reason. Could be the application is out of memory, dumping lots of errors, handling too many requests, or who knows what else. What we know is that it's the very first response from the server that's problematic. None of the external resources or other site content are taking too long to load once disboards responds.
What's disappointing is the lack of communication here. Sysadmin competencies are questionable when an ongoing issue impacting users goes unaddressed for days.