Gally needs to be the go to shooter on his line. He needs to rekindle his chemistry with Galchenyuk. While it would be nice to see the EGG line back in action, that would mean they'd be playing under 15 minutes a game. I'd opt to seperate Gionta from Plekanec and put together these two lines:
Galchenyuk - Plek - Gallagher. There have been countless occasions where had it been Gally instead of Gionta infront of the net, we would've had a goal. This line will be a threat offensively, and should play around 18 minutes per game. It takes a step back defensively, but it should still be adequate with Plek at center.
Bourque - Eller - Gionta. Despite all the flack that Gionta's been getting, he's still a great defensive player. He has a knack for breaking up plays and getting in the passing lanes. He could be a very useful defensive 3rd liner, and would be if not for his salary. Bourque and Eller are also good in their own zone. This could be a very solid 3rd checking line; limit chances in our zone, go strong on the forecheck and pitch in for a goal here and there.
4th line is pretty standard, and since Patches insists on being with DD, let them stay with Briere if it means that we have a great 1st line and a solid 3rd line. Or make a small move to acquire a bigger right handed winger for that line. No one too special, just someone who can crash and bang and provide them time/space.