In the dataset with columns for each individual month, try using the unpivot transform on all columns you would like to end up in your single date column.
The way the unpivot transform works is it takes the column headers in the range of columns selected, and transposes them into row values of a single key column, and takes the row values for each original column in the range of columns selected and transposes those values into a single value column. This is demonstrated below. Column1, Column2, Column3 become three rows in the key column; value1, value2, value3 become three rows in the Value column.
You can see what I mean below:
Unpivoting the above set of 3 columns, each with 1 row value, results in this:
