The problem has gone away. In my Data Flow, in the Excel Destination, I changed it from using the 'SQL command' to the 'table or view' option. Then I clicked the "New" button. First I got a warning (I forgot to write it down). Then the "create table" SQL statement appears. I choose my Excel sheet (Excel_Destination$, which I mentioned in the top post). Now when I run the package, I don't get that error.

I think that when I click "New" that SSIS is rebuilding the internal table that exists within the spreadsheet. That's my explanation for what seems to be a very obscure and mysterious area of the SSIS to Excel realm.

At least I can move forward. I like SSIS when it is working. 😉