If it is possible to run off a PP3 battery for a valve, then it should be quite easy to make a regulator to feed the solenoid. All of these do reduce the chance of motors blowing, and will mean you dont habve to go to the hassle of installing cooling or heat sinks.

You may have less power, but the performance of a 14.4v drill on 14.4v isnt too bad, and should be fine for a LP flipper bot.

As Philip said, resistors are designed to turn the enerygy into heat, any resistor able to handle the current a drill motor is likely to draw would be large, and probably affixed to a heat sink, so forget that idea.

If you use 14.4v then you can use two Ni-Mh 7.2v race packs in series, which should give enough power for two drill motors and will be around half the weight of ni-cad packs.

Cheers, Ewan