Seems like people don't like folks camping at elites, but when they see they might get fired, they like the idea a lot less...
I think that two relatively easy fixes deal with the issues people are identifying:
1. If you pick up a rebuild, your 4-year clock doesn't start until the team is 1 letter grade (or 2/3 letter grade, not sure which is fairer) below its baseline prestige.
2. If you win an NT, you have a 2 or 3 season "grace period," before the 4-year clock starts again. Maybe if you lose in the finals, you get a 1-year grace period before the clock starts again.