Okay, so this is just off the top of my head because of course I’ve had a phone call: “All right, M, what would you do with this?” And I haven’t had any kind of time to really think about it, but . . .
We’ll skip Gallifrey for the moment. These things just tend to come off as cheesy anyway and will limit the audience potential. Also: budget concerns. So let’s get right to the Doctor being on Earth. Wherever, doesn’t matter, pick a place to film (a city, though; the more people in harm’s way, the better our hero comes off when he saves them).
So what’s he doing? Trying to fix the TARDIS, I suspect, so we’ll start him off gathering parts somewhere—a junk yard, a landfill, a Dumpster, doesn’t matter, just somewhere there might be, say, bums or homeless people or sanitation workers because here comes our inciting incident: the Doctor is going to do something strange and amazing that will set off a sort of panic. Pretty soon authorities will be hunting for him, and meanwhile he’s desperate to fix the TARDIS and what? Get back to the Time War maybe, something like that.
Yes, yes, so then we need to introduce our companion. Probably female. Someone who recognizes him from the news reports or the YouTube footage or whatever is going around. Ready to call the police when she runs into him, but of course he does something either to save or impress her, and she takes that split second to rethink things. Curiosity, cat, satisfaction, etc.
There will be the whole bit in which she’s not sure if he’s crazy or what but finds herself helping elude the authorities anyway because he swears that blue box can time travel—if only he can fix it.
We’ll want another threat as well, something unfriendly coming at the planet. The Doctor will get the TARDIS up and running, and he’s all ready to get back to that Time War, but finds himself unable to leave Earth in peril. So he takes up precious minutes/hours/days thwarting whatever threat we’ve stacked against the humans, and only then will he be able to get back to Gallifrey . . .
But he’s just slightly too late.
He’s a homeless drifter, has a working TARDIS and a companion, and off we go to the next film (assuming there is one).
See? Not bad for sitting at my desk while two small children scream at me to help them with their puzzles and can they please have some doughnuts.