I was able to get HTTPS working, although to be honest I'm not sure what did it. I opened a case with TAC and tried additional suggestions such as creating a local cert, regenerating the system generated cert etc. I tested after performing all of these steps and I beleive it started working AFTER I deleted the local cert that I created. Not sure what bound things up to start with, but it is good to go.
It is worth noting that this is an essentially new, out of box, switch with minimal configuration. Possibly a bug with the version of Junos? The issue was present at 14.1X53 D10 (installed from factory) and with 14.1X53 D35, which I upgraded to.