I think they put themselves in a real bind here. Even if they fired MacPhail yesterday, it would be difficult to just hire a new President quickly. But mostly, MacPhail is in no way being forced out. He's in charge of finding his replacement, just like Gillick was in charge of finding MacPhail (who also had Monty's approval). Middleton trusts him completely and in the short-term they are not holding Klentak's tenture against MacPhail, or Rice. Klentak himself will probably be working on arbitration briefs or processing analytic scouting reports, since it's all on Zoom there won't be any bad optics to him being around.
When it's all over and (if we're lucky) Theo Epstein or Neander or Thad Levine (who is not the President in Minnesota) is in charge MacPhail will almost certainly remain as an advisor. Heck, we're not that far off from Ruben coming back as an advisor!
They really can't hire anybody in time for the first round of off-season moves if they want an actual President of baseball ops. Theo's not yet in play (not that I think that happens), Neander and some others are still in the playoffs, and Luhnow still can't be interviewed.
In that recent interview Arbuckle implied that he and he alone made all the first-round picks during his time so hopefully they just let Barber do his job. Of course he's still got Almaraz and Gillick, the guys most responsible for Randolph and Moniak, to "help."