Honestly, the two shows have such different formulas in how the action is handled that I don’t really see it working very well.
Like obviously, there are writers talented enough to make anything work really, but I think the two shows do have tones that would make an episode like this just be pure fan service.
I think it would work best as like either its own self-contained little mini-series, maybe one where the doctor finds himself in the Star Trek universe and winds up traveling and interacting with multiple eras. Or a one shot special that exists outside either shows season
That’s generally been my opinion, too - two great tastes that likely wouldn’t taste great together.
But for the sake of arguing with myself, they were able to make the SNW/LD crossover work, and that arguably has just as much tonal whiplash, if not more, despite the shared setting.
