The solution you're looking after is named : X2GO as it allows to connect almost in anyway possible, included XDMCP.
It is waaay beyond VNC as it takes it's root in the NoMachine code, thus compressing and sending just what is needed opposite to VNC.
ie: between 2 machines, both on ADLS2 with download/upload ~5Mbps/1Mbps, I access the other machine through the web with 16M colors just a tiny bit more slugishly than a LAN connection…
Make sure you have both machines with the same user (although, this isn't mandatory, but a bit more complicated to set up), follow the howto from x2go.org and you will never come back to VNC… ever :)
I forgot one thing : it uses SSH as a transport.