Start with an Auralex SubDude isolation platform under the sub. They really do a good job of reducing rattle and rumble.
If your phono pre lacks a subsonic filter that may be part of the problem.
I have had a few turntables in this room since using a Sub Dude under my sub and have never experienced rumble or speaker cones flapping all over the place and my phono pre has no Sub Sonic filter. I'm temporarily using an old file cabinet with 60 or 70 pounds of lead and I am lucky my TT seems immune from bass and footfalls.

