Your solution was to go to more efficient speakers. Mine is a big amp with the gain turned down. Those seem to be the only work arounds.
Once I added and calibrated a sub, the difference was about 7 db hotter for the speakers crossed at 120 Hz. The sub (bandpass mid bass) is under the foot of the bed pointed at the dresser that the speakers sit on. It's out of the way too. Like the whole thing 'works' just the way I need, at a price point I could meet so I'm good. For more demanding applications ... I don't know.
Like, how much does no hiss cost?
I bet it's more than a buck and a quarter plus shipping.