I agree that acoustic treatment is optimum, but also acknowledge it may not be practical.
My going splat on this topic ...

Weogo's thick theater curtain suggestion helps and may be cost effective.
It has the advantage of working along the lines of what you are already thinking (curtains/fabric)
and, I assume, might be acceptable to the dance hall's owners.
(Bill Porter ... if you see this ... what are your thoughts on Clarkston's curtains?)

The gym mats idea is one I hadn't heard before.
I assume leaning them at an angle helps diffuse the sound up away from dancers.

There are numerous DIY sound panel projects on YouTube.
Here's one analysis: https://www.youtube.com/watch?v=HwaZhT_CrYI
Also, a quick search came up with DIY sound panels costing $7 to $30 each.
Of course, those are mid-sized (not large) panels that would go into a
normal house room and not a gym. BUT, every bit helps. The Sautee gym
has sound panels on the far wall and fabric (not super thick, but fabric) on other walls.
Putting sound panels on the far wall will help with main PA bounce back.
Putting sound panels behind the musicians helps with musician monitor bounce back.
These can be artistic with a little effort and add to the overall visual space.

Your sound system setup can help ... a lot. Lower frequencies are not directional
but higher frequencies are (more) directional. Sautee gym uses 4 "J" line array (hung high)
speakers per side with the speaker targeting the back wall set to just catch a tall person's ears
standing at the back wall. That's $25K worth of sound gear and installation that's
not likely viable, besides being permanently installed.

Another route, my GO-TO, is multiple quality speakers with delays.
Theory is quality gives clarity (at volume if necessary) and multiple w/ delays
gives (more) even sound coverage with least sound energy going into the room
since not trying to push clear sound all the way to the rear from the front.
Most recently I've happily run sound in a typical mid-sized basketball gym box
(happy meaning caller and music clear, dancers not struggling to hear, weekend loud)
for an anniversary celebration day of dancing with:
    2 RCF NX L24As for front of hall mains (30 degree vertical pattern, slight bias down)
    1 RCF TT 12" sub-woofer to one side by one of the mains
    1 RCF TT 051A front center fill (fill space left by mains to some 20' out, not loud at all)
    2 RCF TT 10A iis down hall side fills on delays (70 degrees vertical coverage)
I've had good results using this setup in several gyms.
In theory, the front of hall mains are barely audible in the back of the hall w/o side fills.
In theory side fills just fill the back area.

Bill Porter, in Atlanta, has rigged (in the past, don't know his current fav setup)
2 front of halls, 2 mid-hall side fills, 2 back of hall corners pointing up hall.
Theory says phase issues should be a problem but in practice this rig works
to minimize overall sound energy bouncing around. (of course using delays
off a Mackie DL16s and a click track to set delays).