Here in New Zealand we run foam tires all the time.
Use nitro TC foam tires not Jaco or Parma indoor tires.
Jaco nitro shoes, and GRP (fast tires, Ellegi,Power tyres) will work very good.
Try using 37s all round would be a good starting point i think. And then you can see if you want to go harder or softer, depending on how much grip there is. This might sound strange but also try 26mm tires front and rear i think you will find that it works a little better than wider tires on the rear.
Hope this helps.