Thanks for the reply.
My boot size is 13 and I have large cartel bindings.
Unfortunately I don't actually have a camera right now (not even on my phone), but I'll try and get my hands on one and upload a few pictures of the mounted bindings tomorrow.
I did consider whether the problems I was having are due to incorrectly mounted bindings. After I first experienced the lack of grip on the toe-side, I made a rushed attempt at moving the bindings further towards that edge. Currently the "gas pedal" does hang over the side of the board by about half a cm and my foot protrudes out quite a bit further still, but as far as I'm aware there is no toe-drag.
I'm wondering, maybe I tried to correct the bindings in the wrong direction. Should I have tried to move it further towards the heel instead?
Anyway, I'll upload the photos tomorrow.