The czar/president of hockey ops idea seems like the right first move to me. Firing JB in the near future and installing, say, Randy Sexton as interim GM while you search for someone new does nothing to change the perception that TP is too quick to fire people, and probably limits the pool of experienced GM candidates who are willing to come here.
With a good president of hockey ops, you start to change that perception. Future GM/coach candidates may not trust TP at first, but hopefully they'd trust the czar, who has established relationships in the league. I hope TP would be willing to make such a move. Maybe he would be wary because of the way things went with LaFontaine. Maybe he would think it unnecessary because of the success the Bills are having with a similar organizational structure. Based on the way other teams around the league fill positions like this, we'd probably be looking at someone with some history with the organization.
I remember how excited I was the day we hired LaFontaine and would probably feel a similar burst of energy (and, dare I say it, hope) if something similar happened again. That would be nice.