I agree on David Lee. Tyrod might not be heeding advice from him (can't say anything with certainty) but his track record is pretty poor. Wouldn't carry him over. In fact, I would probably start from scratch with the coaching staff.
I'm not against ripping the FO up and starting again but I'm good with keeping Whaley, Monos and Rob Hanrahan (Director of Pro Personnel). I don't see the team as talent-deficient in a lot of areas, I put quite a bit on coaching.
As HC, I want an offensive-minded guy. Leading candidate for me is Jim Bob Cooter, I think his work with the Lions has been superb. He's got Stafford playing smarter, I think he could use Shady in the passing game the way he currently uses Theo Riddick. I have faith that he could either guide a rookie QB and limit the negatives of a journeyman vet. Cooter can install any OC he's comfortable with, anyone that's on the same page with him philosophy-wise.
My current pick for DC might get laughed at given recent years but I'm taking a gamble on Gus Bradley (I mean JAX have to fire him, right?). He's clearly not HC material but I would bring him in to install a similar Cover-3 heavy scheme that he's run in Seattle and Jacksonville. That forces us into the 21st century with an athletic roving FS.
I'd even try and poach Pete Alamar from Stanford to be the ST coach. Had two years at Fresno State, they blocked 18 kicks in those two seasons. Good track record with the return game as well.