Had a 45 minute conversation with Crutchfield regarding this. Basically, they recommend leaving the factory JBL amp intact and installing a (fancy) line out converter after the factor amp (specifically the AudioControl LC6i 6-Channel Factory Integration Unit). From there, run the lines into the aftermarket amp and on to the speakers. It's certainly not how you would design if starting from scratch, however, the factory Nav/head unit relies on the factory JBL amp for power and perhaps some other things.
I got the impression this would improve the sound quite a bit, but it would never be top notch. Given the well documented constraints of having to retain the factory Nav/head unit, this sounds like a decent option. The other option (for me) would be relocating the factory tape deck and adding a new aftermarket head unit. However, I haven't been able to locate any detailed instructions for how do to this.
P.S. The Crutchfield advisor also said a line out converter with DSP (like the JL Audio Fix 86) MAY improve the sound. This would add around $200 to the total cost, though. This would clean up the factory signals, but assumes the factory JBL amp is working 100%.