I think you are too worried about handedness on D. It does not really matter if guys are right or left handed shots, just that they play well on a side and that the coaching staff utilizes them on that side.
Remember the defensive juggernaut that was the Stanley cup champion New Jersey devils?
Scott Stevens -LHD
Scott Niedermayer -LHD
Bruce Driver -LHD
Ken Daneyko -LHD
Shawn Chambers -LHD
Tommy Albelin -LHD
An outstanding D core, who had all LHD, but just had several guys that played very well on their offhand side.
It isn't that this team necessarily needs to balance the handedness of the D core so much as the coaching staff needs to get a clue and properly evaluate who plays well on what side, which they don't seem to be capable of doing from the looks of things.
If I am coach, I would be looking at the D core and thinking guys that are comfortable playing the rightside - Dahlin, Clifton, Samuelsson, Jokiharju. I don't see any reason why Byram should be playing on the right side, and that is more a coaching issue than a personnel issue imo.
As for the veteran mentor thing, yeah, I totally agree and have been saying the same thing since Risto was the teams #1 D.