Well, it seems like I have the answer to the question of whether it is possible to work VHF DX during tropo openings from my location behind the Lake District Hills.
The map above shows the 2m opening that is apparently going on as I type this. What I can hear in my receiver with my beam pointing east is... precisely nothing. :(
I was delighted to be able to work down into Spain and Portugal in June during some big Sporadic-E openings, even though I heard and worked a lot less than people elsewhere in the country. I guess that was possible because Sporadic-E clouds are high enough to reflect signals over the hills to me. Tropospheric ducts occur in the atmosphere at heights of only a couple of thousand metres, so I suppose a clear path is still needed.
I would really like to move back to Essex!