Well done, Sherlock! Good to know the problem is now fully explained. All that remains is to find a fix ...
I'm afraid https is not (yet) an option with jobe. I have had repeated requests for it (you'll find some in the forums) but have always resisted on the basis that the gains would be negligible from a security standpoint and the cost would be extra complexity, lower performance, and at least one more point of failure (expired certificates). However, I think I'll have to accept that there is actually one significant gain: compatibility with common IT service department policies, even when these are largely meaningless in the context of a Jobe server.
I'll look into it when I next have some development time (I'm currently teaching two courses). Until then I think you'll have to try to get the http proxy limit raised. It's hard to see how ITS could justify a 1k limit for HTTP but a 4M limit for HTTPS.