Lo and behold, this morning I was finally able to download all my stuck Cox inbox email messages to my Mozilla Thunderbird software--for the first time since February 1st. The download included the "bad" message that was apparently causing the problem. Hopefully this restoral of normal email retrieval will continue.
Since I had received conflicting information from Cox Tier 2 Technical Support personnel last week, I called them this morning to advise them that I am again able to download my incoming messages from their server and to inquire as to what they did to correct my issue.
The Tier 2 rep advised that in my case, they were able to go into the appropriate server handling my email account and re-encrypt the single incoming message that was causing the "Error 127.0.0.1" block (they were able to do so by "changing permissions" on this particular message). This effort was successful. In this regard, she also informed me that not all reported instances of this type of trouble can be fixed like mine--instead, some customers will indeed have to wait until full migration of Cox email accounts to new servers is completed (with target date of next month, March).
So, from how I interpreted the Tier 2 rep's information this morning, I was fortunate in that they were able to resolve my individual situation.
Bottom line, they did follow up with my trouble tickets. That fact is encouraging. However, I still am not pleased by the differing responses I received last week during my four separate contacts with Tier 2 Support when reporting/discussing my issue and the lack of any definitive follow-up feedback regarding corrective actions on their part.