Hi Neil,
Yes - high summer is not the season for laminating!
First you can pour the mixed epoxy into a wide flat tray. That way the heat from the chemical reaction isn't retained so much, so the resin warms up less, so the reaction goes slower, so less heat is made, etc etc. Also don't hold it in your warm hand. Also don't leave it in the sun. Also you might want to place it on a cool floor, in draft, etc etc Every little bit helps. Each 10 degs it is cooler doubles the time to harden (poss not working time, but it definitely lengthens it)
Second, if you are reasonably careful not to put too much on you can pour resin on and then spread it out.
Third, I would not recommend trying to wet out two layers at once with a wet layup. There is room for it to look ok but not be ok. However when the second layer goes on it will partially wet out from the resin in the layer beneath.
Good luck! I have never used ice-water and all that to keep mixed resin cool, but it may work.