Is there some law out there that says that every episode of either series has to be in continuity with every other episode? Is there any particular reason they couldn't do an episode that is intentionally set outside of both Trek and Whoniverse canon? There's really no need to match up timelines.
Or, the simple solution.
Treat them as two separate universes. We know that the TARDIS can travel into other universes (E-Space, Pete's World).
Or the even simpler solution.
Don't give a shit how they fit together. Let the fanboys have apoplexy and aneurysms trying to figure out how they work. Focus instead of telling a story