Yea, they make a siped tire just for applications as you described, a bit more spendy, but tires last longer and it's safer. Contact any industrial tire supplier and they will know what you're talking about.

According to our experience, nothing will help definitely.
You can reduce the slippery factor by using the tyres with the treads (if they are rubber) or, eventually, use the special Vulkollan bandages with quartz inclusions - they behave a bit like sand paper (surfaces!) but this may reduce the slippery problems.
As far as I know Raeder-Vogel makes such tyres.