Now that Shalka!Doctor has been acknowledged in the show, I am 100% back in on my old theory that he:
a) is a post War in Heaven Ninth Doctor (linking with his intended backstory with the Time Lords in the matrix),
b) is the same incarnation as the "Cabinet of Light" Doctor, with the Eighth Doctor being the one who was betrayed and shot in the back,
c) erased himself in restoring Gallifrey / splitting the timeline from the War, but due to the intricate timelines is kinda remembered by the Doctor as another life within Eight's lifetime. This is also why he shows up in With All Awry / Now or Thereabouts in the Eleven Day Empire with the post Ancestor Cell amnesiac Eighth Doctor and the post Time War Ninth Doctor.
(Weirdly this is also very similar to the recent fate of the Nicholas Briggs Doctor - what this means, I don't know. It's interesting that this may be a pattern that repeats: the Briggs!Doctor erases himself to bring back Gallifrey, the Shalka!Doctor erases himself to bring back Gallifrey... if they hadn't managed to 'trick out time' this would have been the fates of the New Who Doctors too in Day of the Doctor... erasing themselves to give their wartime incarnation a new future...)
While I'm all in that he links somehow to the post-War universe, this does leave us in an awkward position where his exact existence depends not just on exactly how that happened, but also leaves us with the question of where exactly he emerges from the whole mess.
My original interpretation was that he was simply a post Gallifrey Chronicles Ninth Doctor, who was later erased restoring Gallifrey,
But I also really like the idea that the Jacobi!Master seen in Scream of the Shalka is the "same" incarnation we meet in the Time War / Utopia, even if his history might be quite different. Compare this with the post biodata virus Fourth Doctor, who was born under very different conditions, but is still effectively the incarnation we know. While this works extremely well with the interpretation that Romana III / Trey's Gallifreys are one and the same and the War started not during the Grey Eminence erased VNAs!Romana Presidency, but the delayed BF!Romana Presidency, it does somewhat clash with my original idea.
Assuming their timelines sync up (which tbf isn't necessarily the case, especially as the War Master has been zipping his way all over the timeline - plus we have the 'child' War Master to account for) this would seemingly place the Shalka Doctor MUCH later in the timeline: nearly to the point of Night of the Doctor (or at least around the time of the current Eighth Doctor audios), with the Android Jacobi!Master still succeeding Macqueen.
But as far as we can tell, Shalka doesn't really fit with the future Doctors during the War (the ones leading up to the Relic anyway, though we may also need to note the rejected "The War" novel that would have featured COFD!Thirteen too). I guess he could emerge from one of the other(?) alternative Eights, like "Grandfather Paradox" or the Infinity Doctor? This does somewhat go against the idea of him still being part of the Doctor's history though.
Hmm....
I guess for now, my interpretation has to be that the Shalka!Doctor is indeed post-EDAs, and the Shalka!Master is a remnant of the War, from the Doctor's future, with the timelines indeed still being out of sync? This does at least continue to work well with the idea that Gallifrey is still around in the post Ancestor Cell Eighth Doctor's "present" but he's still living in the unerased War timeline - so the Shalka!Master is native to the post-War universe, but the Shalka!Doctor is not.
