The best answer is to save your money and not treat the walls. A dropped (suspended) ceiling does very little to soundproof. The tiles are lightweight, and not nearly massive enough to stop serious sound. The 4 Elements of Soundproofing. The tiles are not designed to be soundproof. They are designed to lower the echo underneath them. So the person in the office cubicle next to you can’t hear you as clearly. The tiles are also not sealed, as they lie loosely in a lightweight track.
You could have the most impressive soundproof walls in the world, but you will not see their value if the dropped ceiling is such a limiting factor / weak link.
One ceiling option is to drop the framing down 2” or so, and then attach drywall. This will align the ceiling drywall such that you can run the drywall all the way to the foundation itself. Then seal the drywall to the foundation. You lose ceiling height, but effectively put a lid on the room.
The other option is to keep the ceiling height, but build decoupled walls. This is covered in depth here: Building a Room Within a Room