Why not ask the landlord to fill up the gap in your brick wall with... bricks.
close that wall and keep mass
If only that were a possibility... the landlord is not the accomodating sort. He only wants to do the minimum necessary to partition the spaces. The rest is up to me. I considered the possiblility of using concrete block to close off the opening but it would a) require a contractor and therefore some $$$ as I have ZERO manonry skills and b) from what I could the sound isolation performance isn't much better than what can be achieved using lumber, fiberglass and gypsum.