I would like to provide an update. The software upgrade from Sprint Zone has not reliably fixed the death grip issue. I could not consistently reproduce the death grip problem after the software upgrade though. In other words, the signal sometimes would drop substantially and sometimes just drop a little.
So I took the phone to a Sprint store. The guy at the Sprint store had the same phone. So we compared our phones side by side. When he gripped his phone at its bottom, the signal would drop but then went up quickly. My phone, on the other hand, stayed low. Since I bought my phone at Best Buy, the Sprint store couldn't do anything for me, according to the guy I talked to at Sprint Store.
Best Buy offers a 14-day exchange/return policy. So I went back to a Best Buy store in a different city last night, and got my 3rd HTC One. I was hoping that it would come from a different batch.
I am sad to report that this 3rd HTC One phone has the same problem. It is similar to the 2nd phone in that the problem is inconsistent. Both 2nd and 3rd phones got Sprint Zone update while the 1st phone did not. With the 1st HTC One phone, I could reliably reproduce the problem 100% of the time.
I can't believe that I have gone through this much trouble.....