In the past, Boychuk has shown that he is a more than capable partner for Chara. Those two together (or Hamilton with Chara and Boychuk with Bartkowski) should be a fine solution for the rest of the regular season.
The need IMO is to get a LH-shot to slot into Bartkowski's current role, and who can play the right side if needed as part of a shut-down pair with Chara. In the postseason, Julien can have Boychuk/Hamilton slide down and pair with Bartkowski/Krug, presumably with McQuaid as #7.
Looking at impending UFAs, the crop is pretty thin as far as guys who have the mobility and defensive acumen to slide in alongside Chara - particularly from teams that look like they're going to be out of it:
Nick Schultz (EDM) - $3.5m
Henrik Tallinder (BUF) - $3.375m
Dan Girardi (NYR) - $3.325m
Nikita Nikitin (CLB) - $2.15m
Stephane Robidas (DAL) - $3.3m
Andrew MacDonald (NYI) - $550k
My favorite guy from that list is Nikitin, who I believe is pretty undervalued across the league - very respectable relative CORSI, had a positive zone start differential each of the past 3 seasons, and has started most of his shifts in the defensive zone in the same period. With Kekalainen being a forward-thinking, stats-oriented GM, I don't think he'd come cheap, but a prospect like Khokhlachev and a pick (2nd or 3rd) for him would be tempting.
Tallinder is most likely cooked, but could come cheap (i.e. a 2nd rounder). Schultz is not a very attractive option either.
A lot of people like MacDonald, but he's been consistently among NYI's worst defenders by relative CORSI. He eats ice time, but not especially well.
Guys like Girardi/Robidas would be great to have, but I'm worried that they're cost-prohibitive. Moreover, Girardi's a guy with a lot of shot-block mileage on his body (not unlike Seidenberg) - with what the B's currently have on the books, I would think they're looking at Girardi as a rental. Anything more than a prospect and a first for him given this team's current situation would be an overpay, and I think teams (especially those with long-term interest in Girardi) will blow that offer out of the water.
edit: There's also the Mark Stuart option, but IMO they'd only go with him if they had full confidence in a Chara/Boychuk, Stuart/Hamilton top-4. Which I would doubt.
edit 2: on the non-UFA front, Dmitri Kulikov would be very appealing, but he's likely to go for a lot more than he's worth