I take it you've never been the head of a large organization, firm, or business. In a large, complex organization, managing by consensus is a recipe for disaster. You simply cannot please everyone. The organization will FAIL while you're in the process of appeasing everyone and not paying attention to leading the organization. The leader must make tough decisions based on the information he/she has in front of him/her. Here, we have decades of tradition on our side and, while important to us all, it's not the most important part of TH's job. Winning football games is. TH (and certain of us on this board) have allowed it to become an issue on par with the primary objective: winning games.
Resolving it to satisfy all sides as you desire is not a probable outcome without also destroying the organization.