I think this is becoming a little too 'cast in stone' tbh.
Surely modern managers don't just have one style/tactic/formation.
The first question, for a prospective manager, should be about how they'd use the squad we have/will have.
The next questions should be about how they'd approach home/away games, when losing/winning/drawing, against a team that comes to attack/defend, etc etc etc. In the modern game that can't just be 433 and keep repeating the same things win or lose.
We have to have a manager who can cope with the loss of certain players through suspension/injury/sale and adapt to situations such as teams doubling/trebling up against Clarke. I don't believe, and the managerial changes haven't helped, that we've really 'found our style' and many players haven't found their best positions. That's because the likes of Jobe, Neil, Ba, Rigg, etc, have been asked, at an early age, to play in various positions, styles, tactics.
I agree with you, that we need a good foundation, but think our next manager needs a full season to sort things out.