I just had a 4000NEX deck installed thinking it was the 4100NEX with Android Auto.  I realized my screwup and for now will have to live with it.

When I first was playing with the deck and had my Android phone paired, there was a bluetooth menu and I could use other music players (Like PlayerFM) and it would show information on the NEX and allow me to control it through there.  Now, no matter how hard I try and what settings I change, I can only get the Pandora integration to work.  This is OK, because after I open Pandora I can open PlayerFM and it takes over, but Pandora is still on the screen on the NEX and I have to use my phone to control Player FM.

Was I smoking something that made me think the Bluetooth menu was opened up, or what am I doing wrong that won't allow it to open up now?

You can listen to other audio apps via bluetooth from your phone onto your NEX, but I dont think you can control it, only Pandora.  Just select Bluetooth from the source menu, not the settings menu.

The issue is the Bluetooth menu is grayed out.  The first time I connected my phone it was available, but now it doesn't come up, only the Pandora option.

What type of phone are you using, I've also found out that the 4000NEX doesn't like more than three connections so you may have to go to setting and delete some devices and repair them

I have a Motorola Droid Turbo 2.  My wife has a Samsung Galaxy S6 that I can try with.  My phone is the only device that was paired with the unit.  I have confirmed no other devices are listed.

Since your wife has the S6 I suggest you follow my solution over in this thread to get Android auto feature on your 4000nex  http://avic411.com/index.php?/topic/81835-8000nexgalaxy-s6-edge-connectivity/   I helped them out alot. You just need two apps and a usb cable. Really simple solution.