Counting with Multiple Criteria - Months and Date Differences

Good afternoon everyone,

I have a large spreadsheet with a lot of data that I'm trying to condense into whether a specific job was completed on time or late. In my example WB, on the "Data" Sheet Column A, I currently have "Due Date" and in Column B I have "Complete Date". In the "Summary" Sheet, I am trying to make like a summary page where I have "Completed On Time" and "Completed Late" broken out for 12 months. For each Summary, here is what I am trying to do:

Completed On Time - Count all the items where the Complete Date is less than or equal to the Due Date for each month.
Completed Late - Count all the items where the Complete Date is more than the Due Date for each month.

I would also prefer having a cell reference in the formula to the month listed (August, September, etc.) but that is not 100% necessary. I'm pretty sure this is a SUMPRODUCT formula, but I've very rarely used it in my time so I don't know the many nuances with it.

I have attached a sample WB with some example data points. Thanks for your help!