Convert 52 Week Rolling Forecast to Monthly Forecast

I have a 52 week rolling forecast that I would like to have displayed in each calendar month that it corresponds to. I have come up with a solution where it does lump the data together into months but it is not a smooth lumping of the weeks as some weeks cross over from one month to the next. Is there a way to lump each week into its respective month. My current solution places in some months 4 weeks worth of data and in other months 5 weeks worth of data. Attached is the spreadsheet that I am using. The tab "Weekly Sales" is the 52 week data which has specified the exact dates on the calendar that that week represents. The "Monthly Sales" tab has the 12 week data which has specified the exact dates on the calendar that that month represents. I've tried SUMPRODUCT but that is giving me 4 weeks in some months and 5 weeks in others. Any ideas?

Here is the file.