Yes sir, they absolutely have to have an overcharge protection circuit. Without it you would be seeing the above picture with flames all over the place...
I'm not sure about using Lithium Polymer, at least not the way the RC world does it. Lithium Iron Phosphate, or Lithium Magnesium Phosphate seem like the safest, at least without having to modify your stock system, a simple overcharge protection circuit is really all the iron/mag phos. batteries need.
I'm looking forward to seeing what your results are. Good Luck!
*For freebies you should contact the manufacturer's. Shorai is run by some particularly nice folks..