I think your "schools" approach feels a bit... shoehorn-y at times (in that Rob Hahn might not translate that well to today). Having said that, I REALLY want it to be true. There's something magical, forgive the pun, about early M:tG that, Old School aside is only really present in Vintage.
The "name" schools give a very intimate feel to the game that's very much lacking in modern-day sanitized M:tG. I suspect that's why a lot of us play the format, it feels sort of Wild West-ish to this day.
Having said that, as a combo player combo decks by their very nature are very disparate in a way control and aggro really aren't. Decks like ProsBloom, Metalworker, Doomsday, Dredge, etc. function so differently it's hard to categorize them together. Speaking of which, was there a Type I combo deck before Type II ProsBloom hit the scene? If not, maybe that's a good place to start.
Personally, I like the "name" approach because it has a certain romanticism to it, but I feel like there are functionally infinitely many ways to approach this and I'm not sure that taxonomy matters as much.
I would posit that the key is looking at how a deck wants to win - what does an ideal game of Magic look like for Xerox, for Outcome, for Oath, etc. That I think will give you the best grouping mechanism for decks; the exact cards themselves are subservient to the goal they're trying to achieve.