If covering 70% or so of
the walls with some very dense board (a la MDF) will provide some reduction,
I'll probably try it. If it will provide next to no reduction, then obviously
I'd be wasting time and money.

With only 70% coverage of the offending sound leak, you will basically
accomplish no discernable improvement in sound transmission. It really does
need to be an airtight seal to get real results.

Scott Fraser