The cap space bind is certainly a very restricting factor*, but it's not unworkable. They're already in the home stretch in terms of how much time they can bank space. They're already calling up players whenever they take road trips. Let the players they call up into the line-up, rather than tucking them into the press box. Losing a couple games of Winnik or Wilson or Connolly or whoever isn't going to destroy the team chemistry. It doesn't even need to be the same "regular" sitting each game. These guys are professionals, and the motivations behind these decision can be explained to them. They need to make a concerted effort to get at least 4 or 5 game looks at some of Stephenson, Boyd, and/or O'Brien before the trade deadline to know what these guys can bring at the NHL level in 2017. They can re-assess Vrana and/or Sanford after the trade deadline, and Barber whenever he's healthy and ready.
Unless all the Hershey kids blow the doors off their auditions, they're going to need to bring in some forward depth. Preferably this would be a guy who can help fix some of the secondary scoring and powerplay concerns and be a regular in the line-up. They also need to bring in a depth defenseman almost regardless of what happens with the Hershey players.
The wonderful thing about this new CBA is the ability of teams to retain money. If they're getting UFAs or players with one year remaining on their contract, retaining money should not be a huge issue for the other team. If they're bringing in a particularly high contract player, moving Winnik or Connolly should not be a gigantic hang-up. They have numerous PK players who have excelled this year, and no regulars (forwards or defensemen) on the Capitals PK are giving up more goals against on the PK than Winnik.
This core group has not shown the ability to overcome the adversity of the playoffs in the past. To me that means we need to ensure we have enough additional depth to overcome that adversity. If that means pushing one or two of the current regular 12 to the bench, so be it. Competition and accountability is good. Guys like Connolly, Winnik, and Wilson aren't some world beating caliber of player that cannot ride the pine during the playoffs. If they have a legitimate fit for some of their historic playoff weaknesses (secondary scoring, powerplay, depth defense), I would not hesitate to make that move.
*Remember that contentious $500K above comparables they put on Wilson's contract that certain posters kept saying wasn't a big deal?