Measure using time not totalizing - Complex one.. I guess.

Hi, chlxco 

According to your description, Is the 'total' displayed incorrectly?

If yes, you can try:

Total Hours =
SUMX (
    SUMMARIZE (
        Table,
        [Start Date],
        [End Date],
        [Time x Month],
        "a",
            CALCULATE (
                SUM ( Table[Time x Month] ),
                FILTER (
                    VALUES ( Table[Start Date] ),
                    Table[Start Date] <= MAX ( Dates[Date] )
                ),
                FILTER ( VALUES ( Table[End Date] ), Table[End Date] >= MIN ( Dates[Date] ) )
            )
    ),
    [a]
)

Did I answer your question ? Please mark my reply as solution. Thank you very much.
If not, please upload some insensitive data samples and expected output.

Best Regards,

Community Support Team _ Janey