This thread is very interesting. Not knowing what the piece in questions looks like intact I can't say for sure, but is it possible that originally the builder of our holy grail was trying to use this piece of the booster as the emitter itself?
I'm guessing since it fits inside the BP that maybe it would've looked unbalanced so he just shoved the BALANCE pipe over it and voila! Let's look at the parts used, the "gear" and the grenade are obviously both from weapons, the clamp was probably at this point already used on another lightsaber so it made sense to try and use it again. Going with my little theory between the clamp, the grenade, and the booster you could build the lightsaber minus the pommel (including using that booster part as a first draft of an emitter). What I'm saying is at this point you could've gotten all the parts from 2 bins, a weapons bin, and the graflex bin we know they loved so much.
Add a few finishing touches (BP and pommel) and we got ourselves a laser sword!