Might be best to wait to trade Barnett anyways. We have zero leverage right now anyways, because teams now that we very well might cut him at some point. My guess would be that a training camp injury (if there is a training camp) for another team's middle LB might precipitate a Barnett trade. Who knows though, Bishop or Hawk could easily get hurt in camp (if there is one), in which case it would be nice to have Barnett.
As far as the draft goes, the only veterans I remember Ted trading for picks were Javon Walker, Corey Williams, and good ole Brett. I don't think he's opposed to the idea, but it would have to be for the right deal.