You may consider having two logfiles. One containing debug information for you, and another containing information for the solution center. They may be satisfied just with the "RuntimeException: The Sky Is Falling" line to allow them to determine that this is something unexpected that should go to the developer.
You may also want to have an outer try-catch construction which catches all Throwables and try to provide information for the solution center. E.g. for an SQLException, "This is an error with the database, ensure it works properly, restart the applciation and raise a ticket with the developers."
In other words, provide as much information about the situation as you can up front, and in a clear language. This might be a good team effort for a day or two.