Try the dual PID option first. It's promoted as a feature so you can have one PID for heat, and the other for cool, but it doesn't matter. The controller will switch to a different PID based solely on a setpoint.
Tune the second PID at -285F. Switch to the second PID about 5-10% into your last rampdown. You don't want it to switch PID parameters at a setpoint, or it will 'hunt'.
Fuzzy Logic was the wonderful new thing that was going to save the world, but it didn't turn out that way. Some are better than others, but most will agree nothing can replace a well tuned PID.
Try it to see if it helps, but don't be surprised if it's not perfect.
You can't always trust Autotune. Use it to get numbers close, but don't be afraid to do a little manual adjustments to get it perfect.