I mean, while they can block most things, to give people a usable experience they're going to allow http and https traffic through, and they can't really proxy https because of the TLS layer.

So for universal chance of success, running openvpn tcp over port 443 is the most likely to get past this level of bad. I guess they could block suspicious traffic in the session before TLS is established (in order to block certain domains). OpenVPN does support traversing a proxy, but it might only work if you specify it. If their network sets a proxy via DHCP, maybe you could see that and work around it.

I did have fun working around an ex gf's university network many years ago to get a VPN running over it. They were very, very serious about blocking non-standard services. A similar "through" the proxy method was the last resort they didn't seem to bother trying to stop.