In my opinion, the Bruins have more of a 3rd line dilemma than a 4th line one. Pick the 3/4 best 4th line players on the team and put them on a line. Something like a Kuraly - Nash - Acciari/White 4th line. A dependable defensive line that has speed and some grit.
The lack of a dependable and consistent 3rd line is what is ailing the Bruins more than a 4th line. The lack of a 3rd line is putting more pressure on the top 2 lines which currently and may still contain two rookies in the foreseeable future. Where do Beleskey, Spooner, Vatrano, and Backes fit on the team? If the Bruins had the Beleskey and Vatrano of two years ago, an effective Spooner, and a better Backes, there may be a solution there for the 3rd line, but apart from Backes who has started the season on IR, it's hard to see where the other 3 fit or if they become an effective 3rd line unit.