Perimeter walls, ceilings and sound insulation
The insulated partition wall is the primary means of attenuating sound transmission. The adjacent concrete structure provides a flanking path for sound to travel around the edges of the partition, so sound needs to be prevented from reaching the concrete. Normally, one only needs to insulate about 5 feet from either side of the partition to mitigate flanking paths. Due to reverb problems, insulating the entire area could be warranted.

Despite all the added insulation, you will still have reverb problems unless the new finished surfaces are selected carefully. Don't forget the floor can also be a flanking path. Carpet and padding will help. Saw cutting the floor slab under the partitions would also eliminate the flanking path, but could cause other problems if the sub-grade is unstable, so consider this approach carefully.