DAX Formula: Inventory QOH in reverse

I decided to take a shot... Using the data you provided I had to add a row for each category as a "beginning" balance.  From there created an index using EARLIER (well, variables defined before the calculation which is the same as using EARLIER)

Index = 
VAR CurrentCategory = Table1[Category]
VAR CurrentDate = Table1[Date/Time]
RETURN

CALCULATE(
    COUNTROWS(
        FILTER ( ALL ( Table1),
        CurrentCategory = Table1[Category]
        && CurrentDate >= Table1[Date/Time]
        )
    )
)

That tells me how many rows are less then or equal to the current row's data/time, and in the same category:

So then I can use that as a reference point of what came before the current row:

QOH = 
 VAR CurrentCat= Table1[Category]
 VAR CurrentIndex = Table1[Index]
 VAR CurrentQtyChg= Table1[Qty change]

RETURN
CALCULATE(
    SUM ( Table1[Qty change]),
       FILTER(
            Table1,             
            CurrentCat = Table1[Category]
                && CurrentIndex >= Table1[Index]
        )
 ) 

Then the final output:

Maybe what you were looking for?