Is it possible to share a packaged workbook with this small dataset included? This will help us help you. My first thought here is to modify the dates in the date by four days such that all of the data for a 'fiscal month' falls within the same calendar month in Tableau.
Shinichiro Murakami created this helpful workbook as well that I think you might find useful - Optimized Combination of "Fiscal Calendar Table" and "Tableau's calendar calculation"
I hope that helps.