I have a Lumia 950 XL and had exactly the same issue with builds 10.0.14393 on including 10.0.14393.67
I found that If you join the insider ring Gadgets updates to version
4.4.1607.11000 4.3.1607.5001
This version works properly
If you still do not have any joy set your language and region to US and let it install the language update.
Then set language and region back to what they were before.
NB I had to wait a few hours before the update to Gadgets came through.
Ewan, as I've experienced the same problem on the 10.0.14393.67 Windows 10 Mobile Anniversary Update (US language and region version), i.e., my Gadgets app is stuck at 4.3.10820.0 and thus refuses to either update its firmware or recognize the Display Dock, could you specify which Windows Insider ring have you joined and how long have you precisely had to wait prior to the 4.4.1607.11000 4.3.1607.5001 Gadgets app jump? Perhaps the answer may prove beneficial to many... Thanks!