From my experience, the NADA value (from their website) should serve as a guide for the absolute highest price you could expect to get for your ride. That's what the insurance companies in our state use for determining payoff value on total loss vehicles (been there twice about a year ago).

From what I remember, Edmunds tends to show some lowball pricing compared to KBB. Given that, I'd get a price from all three (using the Private Seller option, where applicable) and use a high average from the three as a starting point.

Point of example, using my truck (as it was, stock) as a baseline. 2002 XE 4x4, all power, 88,000 miles, dark blue color, regionally adjusted for the southeast US (NADA gives a national average).

Kelly Blue Book:
Excellent: $10,220
Good: $9,435
Fair: $8,395

Edmunds:
Outstanding: $11,019
Clean: $10,180
Average: $8,443
Rough: $7,555

NADA
Average trade-in: $12,100
Average Retail: $14,725

If I were to total my truck right now (and hopefully I won't), my insurance company would pay the NADA southeast regional average retail value (which, for SUV's and trucks runs a little higher than the national average).