That's interesting, my experience with GH support is the polar opposite – they've been stellar. Particularly their enterprise support went above and beyond when we had issues and never did I feel I got either a canned response or even had to wait particularly long to receive an answer. At one point we had an issue with a flaky load balancer sometimes dropping connections, but the folks maintaining the load balancer were adamant that it was a fault with GHE. Even though I was certain it was the load balancer, I reached out to GH for support and they not only responded with helpful tips to determine whether the GHE instance had a problem, but also helped me build my case that it was in fact the load balancer that was at fault. Turns out the issue was a broken NIC on the load balancer, and GH support were instrumental in helping us figure this out, even though a perfectly acceptable response from them would've been "not our product – good luck; have fun" or something to that effect.
Really surprised to hear about your experience with their support, mine's really been nothing but positive. To be fair, I haven't interacted with them for well over a year now since I'm no longer involved in maintaining GHE. Did support take a hit after the Microsoft takeover?