Your first question about purging talent is difficult to answer. Almost all of our veteran talent signed to long term contracts would bring a cap hit, but there are a few exceptions. For example, Lawrence Timmons was forced to adjust his contract after he went AWOL in the beginning of the year. The Dolphins can release him without a hit. Who else is gone IMO? Easy cuts...Misi, Cutler, Bushrod, Nate Allen, Verner, and Fales.
Something I don't think fans are focused on is our depth and special teams talent. The front office has difficult decisions to make on Aikens, Thomas, Fede, Parkey, Denny. These guys are all core special teamers and good backup depth.
Other veteran considerations. Do we bring William Hayes back? What about Matt Moore and Damien Williams? I personally think we will look to replace Moore and Williams in the draft.
Speaking of the draft, your idea of trading out of round 1 is not a bad idea. The positions I believe we're targeting; LB, OG, RB, FS, are not premium positions. There should be plenty of starter talent in round 2. However, 2nd round talent isn't necessarily less expensive in the long run because those players hit free agency a year or even two years earlier, depending on a teams' choice to pick up the automatic 5th Year option on 1st rounders. The 2nd contract is usually the biggest one for a player.