Happy to report back that after a week on the public beta 11.4 (15F5061d) (this is the version prior to the most recent one), everything has returned to normal on my iPhone SE. Short of installing the beta, your only other possible solution is to make calls via FaceTime or Skype or other service when connected to CarPlay... Siri will set it up for you and for whatever reason, these were clear for me even when using the cord. I am still not 100% convinced this problem is defeated, because my first test after installing the beta I thought was a fail. However, later in the week I realized that I was using CarPlay and no one was complaining. This made me think that maybe it as an app or combination of apps being open that caused the problem--and it was only a matter of time before it returned... Except for one unexpected piece of good news... One person said that I had had a subtle echo for TWO YEARS that he just decided not to bother me about...and now this is gone as well. Will come back to report more if: a) it all falls apart, and b) after I upgrade to the latest public beta.
Just remember--this has NOTHING to do with your car or head unit, and always make sure you read the later comments before following instructions of the inevitable first post that says "Thanks for reaching out to the Apple Support Communities! It sounds like....(your specific problem), I recommend taking a look at this article...." The intention is good, but the laundry list of things to try is posted despite the poster having never heard of your problem before and having no knowledge of whether the list of solutions will work in this specific case. In other words, the helpful person SHOULD say "I have never heard of this problem, but here is a general list of things to troubleshoot." By not saying that, the implication is that following the (often time-consuming) listed steps has solved the problem for some people and might solve it for you. It is often a good idea to try the basics first, but it is even better to read ahead and decide if trying the basic troubleshooting path still makes sense.