What I have learned about setting up live gigs from when I have toured. I often had to set up a band in a room that was designed to be trendy, polished floors, no carpet, etc.
First thing we did was carpet the stage completely, I used to carry 3 rolls of carpet on tour, and hang a thick theatre black at the back and sides of the stage. These 2 things fixed up the sound in a big way, the stage carpet killed any noise from the floor being picked up in the mics and isolated them from the subs to some degree, the theatre black killed off the reflections from the foldback and reduced the slap from the stage that was an annoying number of milliseconds behind the sound that was directly pushing forward improving definition.
As this is an in-house set up, you could construct a broadband absorber/bass trapping behind the theatre black which could be as simple as 100 mm of rockwool and a barrier matt, similar to what is described
here, I would also hang some ceiling clouds of rockwool about 100 mm thick above the dance floor. Please note that all suggested theatre blacks and clouds have to be fire rated and hung safely.
It would be nice to be able to do something with the side walls, but as people lean on them all the time it is probably not practical.
As suggested above, the PA needs to be hung correctly, if this falls on someone expect a big payout and a lot of bad karma. I would look at the front of house having a 12" and horn set up with a sub each side as it look like the front of house has a horn and 2x15" which is a bit over kill. Having better control over the bottom end with the subs should make it easier to clean up the sound because in a room this size you will mostly be try to get a good vocal sound from the PA.
Alan.