FB on the portable HF setup you are building for demos with the Scouts!
Your initial thought was probably the right one – the counterpoise wires should be 1/4 wavelength on the lowest frequency that you will be using. You should try for 3 – 4 wires if you can handle the space requirement, 2 minimum. It will be best to keep them slightly elevated if you can find a way to do that to limit ground losses but they will also work if placed on the ground.
It is probably best to try to setup the entire system in see what it wants in terms of radials. The radiator on your antenna is pretty short for 40m and it looks like it uses a coil/base loading to overcome this. There are scenarios where shorter radials and a greater use of the base loading effect might give a better match. Only way to know if this is the case is to try it.
I hope this helps. Happy to talk with you live some more about all of this. Looks like we may be getting together for lunch sometime soon!