Well we know that in Who's universe Trek is fictional, so I think the best way to do this is to have Q set the Doctor and friends into the "fictional" Trek universe only for Picard, et al, to regard them as cosplayers from that fictional old "Doctor Who" show from the early 21st Century.
Gatiss is the most disappointing of the "elevated fanboys" writers on nu-Who. All his episodes are straight-up by the numbers pastiches of "the kind of thing Doctor Who does," with nonsensical plot threads and tons of unearned sentiment. He seems like a lovely fellow and is quite a charming presence on-screen, but other than "The Unquiet Dead" all three of his Who scripts have been mediocre at best.
Really enjoyed it overall, but I was disappointed that the Doctor never pointed out that you CAN'T kill Hitler, due to him being a fixed point or something. Try to shoot him, your gun will jam...send a robot assassin, and a different time machine will land on top of him...etc.
Yeah it's a real shame that the puppet in "Phantom Menace" was so terrible. It's sad to think that 20 years on, the art of making a great puppet seems to have been lost.
"Come to Me" is a super-sexy and sinister track. Love it! That whole soundtrack was great. "Armies of the Night," "Good Man In A Bad Time" ... I'm going to have to pull out my cassette (yes!) and give it a listen.
Wow, that's got to be the first Dodo costume I've ever seen (posed with the First and Second Doctors), and I've been going to these things for 25 years!
"Banal, beaten to death ideas"? I assume you mean the CIA / conspiracy thriller angle, and not the "what would happen if suddenly nobody could die?" angle, which is minty fresh as far as I can recall.
This movie was being promoted when I was at DragonCon in 1986 (I was there to meet Peter Davison and JNT!). I still have a promotional flier for it someplace - but I never actually recall the movie coming out! LOL
I think it's worth noting that when Spielberg's Amblin was thinking of taking over the Doctor Who franchise in the 1990s, they commissioned new Dalek designs that looked like this: