I've been thinking about this for a while now, my Gibson Les Paul Studio Deluxe has a Corian nut and it keeps getting pinging sounds on the G and B strings. After playing a song the low E string keeps going a bit flat and they're relatively new strings which are D'Addario 11s (11-49). I've been looking at a wide range of nuts and I'm looking at the Earvana Compensated nut (ESP Style in Ivory) and the Graph Tech TUSQ XL Jumbo Gibson nut. My guitar has Grover tuners with the usual Gibson TOM Bridge and Tailpiece. Are the tuning problems coming from just the nut itself or the string gauge?
If the pinging occurs when you play the strings open the nut slots are either too wide or too low and you need a new nut.
You're using .011s, and most guitars are factory set up for either .009s or .010s. Try filing the nut open a little. If that doesn't work, then you'll probably need a new nut