I agree with the “element of the unknown” but I think the Daleks, Cybermen, and Master (at the least) are essential, which is what I’m trying to find. I think without Daleks in the universe, you don’t have the complete world.
I also agree with rebooting it from the beginning. I think there’s no easy way to fill in 25 years of backstory.
As for it being a BBC production with no commercials, well, the BBC seems perfectly content to let it rot. Sure, they’ll okay all the books and audio dramas and tea cozies and finger puppets and coasters and all this other stuff, but as for actually producing the show, they’ve shown zero interest, so I’m assuming this hypothetical production is a non-BBC one. Also, while I give the BBC credit for keeping the show on for 25 years, I don’t like the fact that the entire time they treated it like an unwanted bastard child, insisting it was an unpopular children’s show until the very end. So don’t be surprised if I don’t factor the BBC into the production. I’m assuming someone who WANTS to do the show is doing it.
As for the Douglas Adams humor, I love “Hitch-Hiker’s” and I love Tom Baker, but Adams’ season as sript editor has some awful clunkers in there (and the wonderful ‘City of Death’, which he wrote.) Adams was funny, but he also was more interested in being funny than in making the show good, and hence, ‘Creature From the Pit’. I agree there’s an element of humor, but it’s more like whistling in the dark than anything else.
I never personally got into the purely historical dramas, but I can see something of a place for them. I think that even without forays into Earth history you could have interesting time travel elements, it’s just that the show never really opted to use them. (For example, each time the Doctor revisits a foe, it’s a revisitation for the foe as well. What if the Doctor’s first encounter with a villain is the second encounter for the villan? You get two stories, one in which everyone but the Doctor know what’s going on, and one the opposite. I also like the idea of a story where the Doctor is working against an unknown enemy who turns out to be himself at a different time. There are possibilities out there.)
A female Doctor wouldn’t really do it for me, but I’m not sure why. I suppose for me an essential element is that the Doctor is male. I know in my heart that there’s no reason the main character couldn’t be female, but for me it just doesn’t synch correctly.
I’d ditch a lot of the later aspects of the Doctor’s character introduced towards the end of the show. I think the show works best when the Doctor isn’t an all-powerful being among Time Lords and didn’t leave Gallifrey with the entire Time Lord arsenal in tow. Speaking of Gallifrey, I’d show a little more of their society other than the non-stop corrupt officials, to illustrate his background and why he left.