There are A LOT of teams searching for defensive help this off-season. A LOT.
Boston
Toronto (may need 2 if they don't qualify Liljegren)
Dallas (probably need 2)
Colorado
NYR
Winnipeg
Nashville
Vancouver
NJ
Philadelphia
Florida (needs like 3, maybe 4 if Ekblad is traded)
LA (if they lose Roy)
Buffalo (RD is a big need)
Calgary
Detroit (Need 3 if they dislike Holl)
Utah (need 3)
The list of UFA d-men is pretty scarce in terms of quality...
Roy
Walker
Montour
Zadorov
Dillon
Cole
Tanev
OEL
Skjei
Pesce
Gostisbehere
Brodie
Schultz
Edmundson
Dumba
Kylington
Carier
Hakanpaa
Kulikov
Teams are going to left looking at the lower end of this group with openings in their top-4 and looking to push for the playoffs. I could see Nashville, Dallas, Utah, Detroit, Buffalo and Winnipeg being left with the 'scraps' and trying to determine if it makes sense to sign someone like Schultz for 2 years or trade for Trouba.
The real question is, do teams like that wait or do they get the inclination that the UFA market will not be the place where they can solve their holes and make the trade before 7/1? I am sure Drury and his team would like to make that trade ahead of free agency so they can be aggressive on 7/1 with who they like.
To me, the guy to move before UFA is Lindgren. Sell Utah on his leadership and style of play, recoup some picks. That allows Drury breathing room on 7/1 no matter what to be aggressive and as pieces start to come off the board slowly, let those teams come to Drury to move Trouba at that time.