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Convert them to what: mm/dd/yyyy or dd/mm/yyyy?!
You wrote: Interestingly, all of the dates with "dd" numbers above 12 have dd/mm/yyyy format, and all of the dates with "dd" numbers below 12 have mm/dd/yyyy format.
I suspect that they were input on a system where the actual regional Short Date form is mm/dd/yyyy. Thus, the dates in the form dd/mm/yyyy were treated as text values.
We cannot tell the difference between text and numeric data values in a CSV file because all data are written to the CSV file as they appear in the Excel cells.
Be that as it may, the issue now is: what is the regional Short Data form on your system?
If it is dd/mm/yyyy and you opened the CSV file directly in Excel instead of importing it and (perhaps) setting the column format to Text, then all of the data are numeric dates. Confirm by entering =ISNUMBER(A1) in a parallel column.
In that case, what you interpret as mm/dd/yyyy is actually treated as dd/mm/yyyy by Excel. So you might enter the following in a parallel column:
=IF(DAY(A1)>12, A1, DATE(YEAR(A1),DAY(A1),MONTH(A1))
Copy the resulting values and paste-value in column A.