I agree 1000% with all of this...
...except The Meddling Monk is The Master. Likewise The War Chief for either of them. They're separate characters who were grand adversaries of The Doctor's and deserve to stand on their own.
Pretty sure that was either the actual intention or was one of Terrence Dicks' inventions when he novelized the serial. Or something like that. Pretty commonly held belief.
Yeah, the Monk is definitely not The Master, he has his own style and philosophy that don't even remotely resemble the Master, plus things are just really boring if every timelord villain is retconned into being the Master, there are other bad people with TARDISs flying around, too.
As for my head canons (at least the ones that come to mind immediately):
1). The Doctor played by William Hartnell is THE 1st Doctor, he's the original incarnation of the person we've been following since 1963, born on Galifrey as a child, growing up and eventually stealing a TARDIS with his granddaughter. There was no version of this person before him.
2). The Timeless Child is either The Master or a lie set up by The Master.
3). The Dhawan Master didn't destroy Galifrey, he doesn't have the power. He tricked The Doctor into thinking he did, while the Timelords actually just fled from The Master or for some other reason which The Master took advantage of, leaving a destroyed looking world behind.
4). 99% of spin off material is canon, especially if it doesn't heavily contradict big parts of the show. This includes Big Finish stuff, comics, books, etc. The big exception to this is the really nasty stuff, like the super edgelord early 90s books I've recently read about (Let's not have the 7th Doctor defending men in the past sexually assaulting young girls after a guy pawed at Ace be canon, for example).
5). When in conflict Classic Who takes priority over NuWho when it comes to continuity, and if The Doctor says something inconsistent about things like their age or old characters/alien species in NuWho then The Doctor is just lying, because they can.
6). The Fugitive Doctor regenerated from Troughton and regenerates into Pertwee.
7). The Shalka Doctor isn't canon, that guys device was faulty or detected some left over Great Intelligence stuff from somewhere (screw RTD and his sense of "humor").
8). The Fugitive and War Doctors are the only "secret" Doctors.