Guys, this is just amazing.
Thanks to your suggestion about the IPv4 APN issue, and after a bit of F12 hacking to reveal a hidden IPv4/IPv6 field in the B818's APN settings so that I could select IPv4 (rather than the hidden default of IPv4 and IPv6), all of the applications I mentioned in my first post (at least my work laptop VPN, Tor browser, Skype video, Facebook messenger video that we've tried so far) now work.
Note: I was not able to modify and submit the existing "hard-coded" EE APN profile. I had to create my own new APN profile (using the "+" button), this time calling it everywhere_hacked or something, and using the existing EE APN settings but also setting the hidden field to IPv4.
Also, something else quite curious happened. After I submitted those new settings, the router alerted me to there being a new firmware version available, 10.0.5.2(H190SP1C74). Previously, the firmware page always indicated an error checking for firmware updates. It actually seems that the router's own firmware update code relies on IPv4 perhaps, and fixing (hacking!) the APN to IPv4 only brought that to life.
I cannot say thanks enough. I'm just amazed.
Oh, for info, when creating the new APN profile, you can make the IP type field visible in the console using:
$("#ip_type").show()
So, should I also allow it to do the firmware update? Or keep it on the existing 10.0.2.2? I'd have a very sad face on if it all broke again.