Summing quarters based on monthly data

I work for a non-profit that provides healthcare and we have to report monthly data on productivity. I have attached a very short version of a significantly larger spreadsheet.

Currently, an end user will type in a reporting period on another sheet that P1 will reference. As you can see, the months then adjust to a preceding month to show historic data. The months range is dynamic based on user input. The end user also selects a facility or "All" and the data then gets pulled for each indicator through index/match based on the users input of date and facility. I have simplified it in the sample to just show the data. My current quarterly formula looks at blocks of three months at a time but those are not proper "quarters" (Jan-Mar, Apr-June, Jul-Sep, and Oct-Dec) as you can see entering 7/1/2017 should yield a Q3 '17 of 65, not 172 (sum of 5/1-7/1). I have been trying multiple variations of offset (not included) but cannot get it to calculate properly.
It is not letting me attach a file. I will try in a subsequent post.

I read through about 20 posts and couldn't find exactly what I was looking for.

Any help is much appreciated.

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Attached file