I have fixed the problem through trial and error. The way I did it was simply change these declarations:
ElevenSheets = xlWorkBook.Worksheets("2011")
TwelveSheets = xlWorkBook.Worksheets("2012")
ThirteenSheets = xlWorkBook.Worksheets("2013")
WorkingSheet = xlWorkBook.Worksheets("WorkingSheet")
To this:
ElevenSheets = CType(xlWorkBook.Worksheets(1), Excel.Worksheet)
TwelveSheets = CType(xlWorkBook.Worksheets(2), Excel.Worksheet)
ThirteenSheets = CType(xlWorkBook.Worksheets(3), Excel.Worksheet)
WorkingSheet = CType(xlWorkBook.Worksheets(4), Excel.Worksheet)
I don't know whether changing the sheet names to the sheet number fixed it or the CType
fixed it. But one of them did.