When you say the PA systems is hard to hear, do you mean the “house”-PA? Often they will have their speakers up high and they are usually not the best speakers too.
If you are playing the gig, are you playing over that PA? Or is there another PA, bringing your own perhaps?
When you have anything to say about speaker placement, for rooms like gyms and other echo-rich environments, I find that getting speaker stands with adapters that let you aim the speaker downwards a little and then putting them a little higher than you normally would can help.
Also, if they are bringing in a PA for the event (or if you are in charge of supplying one), getting a (small) line array can be helpful too. Those can be aimed better and usually have smaller “bands” where they project music. Meaning less of the sound is sent up into the rafters and the high windows etx.
Something else that might help is putting speakers on the edges of the dancefloor. Easier to create a good sound on the dancefloor, although you will sacrifice some quality outside the speakers. With the speakers all firing inward to the dancefloor, by the time the sound has crossed the (full) dancefloor, where a lot of the volume is already absorbed by the people dancing, then travels to walls, ceiling, windows and such and then bounces back, the remaining volume is probably not strong enough to create many problems on the dancefloor.
Outside the dancefloor people will hear the echoing bit of course.
Hope that helps.
Greetinx.
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