The best way to send the date to SQL Server is YYYY/MM/DD. So if you switch this:
SUBSTRING(INVOICEDATE,7,2) + "/" + SUBSTRING(INVOICEDATE,5,2) + "/" + SUBSTRING(INVOICEDATE,1,4)
to this:
SUBSTRING(INVOICEDATE,1, 4) + "/" + SUBSTRING(INVOICEDATE,5,2) + "/" + SUBSTRING(INVOICEDATE,7,2))
It should work. I have tested it myself. You also do not need to do the conversion to date in SSIS, SQL Server will do it.