Here's my view on remakes (short version): the story should stay the same because that's what the game is about. If you're remaking somebody else's work then be faithful to the source material. If I was to remake KQ2 I'd not bother because the story basically sucks. It's so cliche and boring. But putting that aside, I'd remove the randomness (like Red Riding hood showing up on a randomiser) because random fucking sucks. I'd remove the circular world (again, it sucks) and probably do what we did in KQ3 and border the world somehow. And I'd do something about that crazy-ass-bullshit bridle puzzle.
The Bridle puzzle is based on two sets of myths Medusa's death being the birth of Pegasus, and Belepheron's attempt to ride Pegasus with a magic bridle. One way to fix that would be to possible scatter clues to both myths elsewhere in the world. Or have the snake say something that might link it to Medusa.
On a side note, does your 'only the games are canon' also extend to to ignore the manuals, articles and other things as well? Noting that you did ignore the timing between KQ3 and 4, by extending it weeks or months between both. I think AGDI largely ignored the manuals in their games too, rewriting them and adding changing things for their purposes.
Obviously some of the manuals and official hintbooks (well largely in particular KQ6, and its hint book), do make references to The King's Quest Companion. The game King's Questions even made multiple references to the Companion (strangely I might add, because my guess most people wouldn't know that the monastery in KQ2's known as the Monastery of the Blessed Wilbury with the game alone). KQ5 NES also makes an offhand reference to the companion in one scene ("Cedric being turned to stone", this change was probably chosen due to Nintendo's strange censorship rules at the time). There is a very minor reference taking from wording from the Companion about 'royal physicians' trying to take care of Graham after his heart attack in the KQ5 or is KQ6's about screen.
Oh did you notice that your 'removing' the circular world in KQ3, actually broke visual continuity? You actually have buildings in the distance that lie to the south of the mountain in the way you bordered things! Like you can still see Three-Bears House to the north, and the port to the north. When they are clearly south on your map! A simple fix would have been to simply paint over those landmarks, or replace them with others. Like from there you should probably be able to see the Oracle cave?
Edit: I guess you did at least paint over the Three-Bears house, and possibly added the cave.
But the village is definitely in the wrong spot!
Edit: No wait this is the image I was trying to remember, there is the bear's house, and the town! Everything is completely out of order of how you located things in the actual world, when you climb down from the mountain, or see on the magic map. That is you have placed most the landmarks from the south see magic map, and ingame world, to the north when they are viewing north from the mountain (the town, the bear's house, the bandit's tree, etc).