It's a trap that a lot of people fall into. The panels, foam, egg cartons, bottles, grids, etc. are great at softening hard sound reflections and reverb, but they do not contain sound to any significant degree. They just make it more pleasant to listen to when inside. The lower the frequency, the more power sound has and it'll transmit through concrete, foam or anything else that is solid. As mentioned elsewhere, if you want real soundproofing, you'll have to build a room that is physically isolated.
After trying and failing in multiple rehearsal studios, the answer was to get a place right near the airport. We can get as loud as we want, as the town has zoned the neighborhood for high levels of (ahem) ambient noise.
This is correct. The only solution is to build a room within a room where there is air space between the two sets of walls. I don't think there is an inexpensive way to accomplish this-
-dj