Seriously, it's going to be fascinating.
As you said, most of the teams in the lottery range desperately need forwards and don't really need D.
Chicago has Vlasic, Levshunov, and Korchinski, and nothing at forward past Bedard.
Buffalo has Dahlin, Power, and Byram down the left side, taking Schaefer would be malpractice.
Detroit has Seider, Edvinsson, and Sandin-Pellika and no one with real upside up front (all their forward prospects are low-upside).
Nashville needs everything, but having never had a real #1C in their entire franchise existence, other than like, one year of Ryan Johansen, I would have to think the draw of taking one 1st would be too strong to resist.
Anaheim would probably take Schaefer, as BPA. NYR is a wrench I wasn't expecting; I'd take Hagens if I were them, but they also need everything.