Well the short term obvious option for any club who have sacked their manager is Conte, that much is pretty obvious, he's the most established manager available. I thought that is pretty much self evident. Like you say he can easily make his system work with these players, as Ole showed against Spurs, so why haven't we gone for him already?
I'm not sure what your opinion is really, whether you think the board are short-term thinkers or long-term. You seem to be claiming they are short-term? I don't agree, at all.
Ole made them believe he was the right man for the job, the entire country were encouraging them to give him a full time contract and they did so after an excellent initial spell as caretaker. They've then done what they want to do and back him, with a long term view that he will bring success in time. They've said pretty much this a number of times and have just given him a three year new deal, pretty obvious they are trying to play the long ball game with Ole.
Of course no appointment has a guaranteed shelf life, but the intention for it to be a long term appointment can and does effect the selection process. If we hired Conte tomorrow it would be viewed as a decision to gain quick results with a likely short term appointment.
If we hired Ten Haag tomorrow people would rightly expect a transition period with a view to seeing results in time, therefore a longer term approach. But the time it takes varies, there's no definitive.
I'd rather we transition to a different style so I'd rather Ten Haag to Conte. Because I prefer the formers style of football.