The Owner had already shown the priority they put on this so the job will probably go to the one with the lowest bid. Not the most effective or the best value, but the lowest cost. Think something like http://www.octasound.com/ or http://www.soundsphere.com/ and a TOA mixer/amp for the gym. So either figure out the lowest cost option that still meets the specs or you're likely wasting your time.
FWIW, I have done dance and fitness studios with recessed ceiling speakers with good results. Some higher quality ceiling speakers and in-ceiling subwoofers can work surprisingly well in such applications, but it's not usually the lowest cost approach.
Yes, the sound system was obviously an afterthought in this remodel plan.
I have done plenty of SoundSpheres and OctaSounds, neither of which I particularly like. The requirement for "loud, punchy bass" implied subwoofers to me.
Bid went in today. We ended up choosing passive speakers, telling them we will have to put a couple of amp racks in the nearby storage rooms. There were just to many advantages to the passive design.
1. Powered speakers on high can't be turned off, except at the breaker box.
2. Electricians don't have to run circuits to every speaker location
3. Amplifiers can be surge-protected in a rack.
4. Etc etc etc.