My VLAN Config looks like this:
http://s972.photobucket.com/user/fixit9660/media/DraytekVLANConfig1_zps41624c93.png.html?sort=3&o=0

I tried moving all the setting up a line and ticking Port 4 in line with Ports 1,2, and 3, but I then lost contact with the Draytek Router?

you tagged yourself out of the management lan - don't that a few times before

looking at your set up id say you have the tick boxes in the wrong places.

Can you try it similar to what I said and see if that make a difference.
Just use vlan0-4 and leave the ones below disabled

OK looking at the LAN>VLAN Configuration page:
This works fine:
http://i972.photobucket.com/albums/ae208/fixit9660/DraytekVLANconfig2_zpsf08c7d0d.png
But the moment I tick the "Enable" VLAN TAG for VLAN 1 with ID 76, my PC in Port one loses connectivity to everything, which is what I would expect. As I understand it, I've effectively turned the Access Port into a Trunk Port, albeit only trunking one VLAN, LAN 1 with an ID of VLAN76. Am I misunderstanding how this works?

so you are using port based and not dot1q?

For Ports 1,2 and 3, yes. Access Ports to one VLAN. I only want to Trunk 802.1q on Port 4.

I wish I had a spare Cisco switch now so I could set it up in our lab and test it out.
it must be achievable