How do I build a sound dampening box for a pool filter?
I think the point to the question was to build a soundproof box more than buy a new motor, although good suggestions for power and such.

From some research on similar topic and some personal experience I have discovered that looking at the mounting of your motors is very important. Sometimes placing a rubber or similar vibration absorbent material between the motor and whatever it is standing on reduces referred vibration and low level tones that are almost impossible to sound proof. Spend time getting the low level vibrational sounds sorted out.

As for a housing, for me their was already a small brick wall around the pumps. I used ply board against many recommendations to build a housing then lined the inner area with heat resistant foam and a lightweight insulation material called "think pink" (in South Africa).

The padding is lightweight enough for me to lift the cover off to get to the pumps and the gap and ambient temperature around the pumps when sealed is cool enough for the motors. Obviously not in direct sunlight helps.

Ventilation is always an issue as direct air exposure permits sound waves to "escape" thus one must use a bit of common sense to allow more ventilation if the pump house needs it to keep the motor cool. 

I would not say the rig is 100% sound proof... Yet... Our bedroom is literally right next to the motor and you can definitely hear when the motor runs. So a lot better than it was. Can't hear the motor from any other room in the house.