Ok I have a cheap solution... when you're putting the ice in the glass, make sure you're got a fan blowing directly at it. This will ensure that any evaporation that takes place will not saturate the air around the glass, as the air is moving. It might be possible to have the condensation evaporate almost as quickly as it formed, which would at least mean it isn't running down the glass and getting the coaster wet. If the air isn't moving around the glass, then the water droplets will evaporate slower, because the RH of the surrounding air is increasing as evaporation takes place.

So yeah, blowing the glass might be enough, but a fan would be much better.