Update: This has been resolved. As deggie suggested (thanks deggie!), I contacted Apple Support for help on this issue. It turned out to be the waterproofing gasket leaking from between the glass and the aluminum body. It does not happen often, but the solution was for Apple to remove the front glass, remove the existing, failing black rubber gasket seal and apply a new seal. They did this in the store while I waited! Apple phone support was outstanding. They had me send several pictures of the issue, ran remote diagnostics on the phone and followed up the next day with a diagnosis and proposed solution.
They then made an appointment for me at the local Apple store and the store tech took it from there. This was outstanding service for a long-time customer with a four year old phone with no warranty or AppleCare coverage. Thank you Apple and thank you to Advisor Marsha and the in-store phone tech! Most companies would be quick to sell you the latest model and be done with it, but Apple stands behind their products, has great people and supports their customers.