Yep, changing out the plastic nut, (and saddle on acoustic guitars) is probably the single most cost-effective thing you can do to a guitar to make it sound better and be more playable. I put buffalo bone nuts and compensated saddles on acoustics and it is amazing how much better they sound than with the old plastic bits. If you are a real note-bender, the rolling bridge, and the Tusq nut will help for sure. Personally I think locking tuners are a step too far, like belt plus suspenders, but yes, good high-ratio Grovers are da kine.
Just one more thing to check: the Tone controls should not affect the resistance readings at the Jack at all. The tone capacitors function by sending high frequencies to ground, removing them from the signal, and the tone pots control how much. Capacitors don't pass DC current, and the multimeter is using DC current to measure resistances, so the caps look like open circuits no matter where the tone pots are adjusted. Neat!