Average Selling Price - Criteria from Multiple Columns

I need to calculate the average selling price of an item in a Sales table. This would normally be as simple as creating a calculated column using:

DIVIDE(
     SUM(Sales[SalesAmount]),
     SUM(Sales[SalesQty])
) 

but my Sales table has additional data, for example the [CustomerID], [SalesRegion], and [SalesType]. I need to find the average selling price for each item identified by these features. For example, I need the average price for Item A purchased by Customer A in an Online Sale, which is different from Item A purchased by Customer A in an In-Store sale.

Originally, I used something like this:

ASP by Item = 
    VAR PriorYear = YEAR(Sales[Invoice Date]) - 1
    VAR CurrentItem = RELATED(Item[ItemID])
    VAR CurrentCustomer = RELATED(Customer[CustID])
    RETURN
    CALCULATE(
        DIVIDE(SUM(Sales[SalesAmount]), SUM(Sales[SalesQty])),
        FILTER(
            Sales,
            YEAR(Sales[Invoice Date]) = PriorYear
        ),
        FILTER(
            Sales,
            RELATED(Item[ItemID]) = CurrentItem
        ),
        FILTER(
            Sales,
            RELATED(Customer[CustID]) = CurrentCustomer
        )
    )

My actual use case has more filters, and I end up running out of memory. My current solution is to use SUMMARIZECOLUMNS to make a table with the ASP, and then I created a key column by concatenating the relevant columns together in this table and my Sales table. This works, but the process is quite slow.

My Sales table has about 3M records, with he Customer and Item tables being in the tens of thousands of records range.

Is there a more efficient way to "roll up" an average by multiple columns?