Thanks, Mohitnow and Vistec. This did work for me.
For users still struggling here is the background of my issue:
Phone: iPhone 6 - 64GB
Car: 2013 Honda CR-V
Issues Observed: Day 1 (Sept. 19) the phone paired and worked fine. On Monday, Sept. 22 I attempted to make several calls which my car hung up after a few seconds, but the calls continued on my handset without issue. Attempts to redirect the call to my car resulted in dead air. I could not hear my caller. They could not hear me.
My first attempts to correct the problem included unpairing from both the phone and the car and then attempting the pairing again. This had strange results. On one attempt once my phone was paired successfully, my car was stuck in call mode. I could not hang up, or access any other audio functionality in the car until I deleted my phone pairing.
I have some thoughts on what might have triggered the issue between Friday and Monday, which might have had to do with some issues I experienced in uploading music and movies to my phone. iTunes seemed to be giving me misinformation on remaining space, which ended up with my resetting my phone and starting over.
Mohitnow's solution appears to have fixed the issue after three tests. We'll see how things go over the next few days.