Well... given that I have the same problem regarding our corporate policy (as a SysAdmin where I work, even), and was explicitly instructed by my superiors I could and should use the idea below to "workaround" some of our policy constraints, I don't see the harm in sharing the knowledge.
https are not ports, they're protocols. Ports have numbers. The default port used for
http is 80 (with 81 and 8080 being somewhat common alternate values), and the default port for
https is 443. There's nothing saying that traffic on those protocols can't use a different port, or different protocols can't use those ports instead of the default protocols.
Given that, there's nothing preventing you from setting up a TS/RDP server at another location (perhaps at one's home, or on one's cloud instance) that listens for incoming connections on a non-standard port for RDP (perhaps port 443) and then attempt to connect to it from behind the corporate firewall by instructing
mstsc.exe to connect out over a non standard port (the same non-standard port being listened to on the other end, like 443 in this purely hypothetical example). Through this RDP session, one could control the remote computer and, for example, run a Java app to execute occasional trades with one's broker. Or anything else that comes to mind.
This may or may not actually work, with the other options that enterprise firewalls have for restricting traffic, but it might, too.
Of course, if you try this, you'd want to make sure the remote computer (perhaps at one's home, or on one's cloud instance) is properly locked down, secured with a strong password on all accounts, with strong firewall rules to prevent being "hacked," is configured to accept RDP connections, is configured to listen on the desired port, and will actually receive inbound traffic, by configuring DMZ or port forwarding rules on the router in front of it, if applicable. And, of course, if you're directing your TS/RDP server to listen on port 443, be aware that it will try to serve
https traffic as well, unsuccessfully, which would result in actual
https traffic on port 443 to the machine in question failing.
If you wanted to try something like this, you could search around here or at SuperUser for answers on how to achieve all of that.