Adding custom PI Quarters to my date table

Hello all,

I'm trying to create a column in my date table that groups a range of specific, defined dates into a PI Quarter. Each PI quarter needs to start with the open date of the first sprint in each quarter, and end with the close date of the last sprint in the quater.  These do not align nicely with the calendar quarter.  

For example, here are the start and end dates for first two PI Quarters of the fistcal year:

PI Quarter 1 : 6/30/2021 - 10/7/2021
PI Quarter 2 : 10/8/2021 - 1/13/2022

Desired abreviated result:

I attempted to use IF and DATEBETWEEN functions, but could not achieve the desired results. 

PI Quarter =
VAR FY22Q1StartDate =
    DATE ( 2021, 06, 30 )
VAR FY22Q1EndDate =
    DATE ( 2021, 10, 7 )
VAR FY22Q2StartDate =
    DATE ( 2021, 10, 8 )
VAR FY22Q2EndDate =
    DATE ( 2022, 1, 13 )
RETURN
    IF (
        DATESBETWEEN (
            Dates[Date],
            FY22Q1StartDate,
            FY22Q1EndDate
        ),
        "FY22 -Q1",
        IF (
            DATESBETWEEN (
                Dates[Date],
                FY22Q2StartDate,
                FY22Q2EndDate
            ),
            "FY22 -Q2",
            BLANK ()
        )
    )

Can anyone recommend a DAX approach that would work here?