So far, the DoH (Domain Name Service over HyperText Transport Protocol Securly 2—Electric Boogaloo) server I wrote [1] works fine (looking over the logs, it's amazing just how many queries mainstream sites make—CNN's (Cable News Network) [2] main page made requests to over 260 other sites and that's after I restricted the number of redirects allowed [3]) except for Github [4]. The browser would claim it couldn't find Github, (although the logs said otherwise), or the the page formatting was broken because the browser couldn't locate various other servers (which again the logs said otherwise).
So I dived in to figure out the issue. It turns out the DNS (Domain Name Service) replies were just a tad bit larger than expected. The Lua wrapper I wrote for my DNS library [5] used the RFC (Request For Comments) mandated limit for the message size, which these days, is proving to be a bit small (that particular RFC was written in 1987 [6]). The fix was trival (increase the packet size) after the hour of investigation.
[5] https://github.com/spc476/SPCDNS