Peter, that's pretty much the approach I'd take if it wasn't worth the time to have three settings popping in and out. Might even try a third compressor before the limiter, having the ratios go gradually from 3:1 to 8:1, and the attacks and releases starting slowish and getting faster and barely knocking off 2 dbs until the last one. I might even put a second limiter on if I can slow the release on the first a bit, and even a few mill on the attack so it's not a brick wall limiter and let the last one be brick wall. If the loud speaker's distortion gets too much with the limiting try a soft clipper to soften the tops before or between the limiters.
I'm a big proponent of adding more dynamic fx instances when a wild range needs to be tamed rather than having two or three do all the work. Having four dynamics FX on the track and four on the master is standard for me if it its a problem program and needs solving.
Expansion might be helpful, I've just not had luck in these situations with multiple voices, because of how much they can jumble up the dynamics of a single speaker while trying to raise the three of them to a more equal ground. Sort of two steps forward for how it brings them a bit together and two back for how it actually sounds