How to handle formula with blank (not empty) cells in column

Hello all.

Please see attached workbook.

I am looking for a scale able (and dynamic) formula to give me the value shown in C10.

The logic is as follows:
- If column B is TRUE, multiply the number in column A by the multiplier in row 2 (columns D through G).
- The multiplier to be used is the number that is above TRUE in columns D through G.
- Add all of these values up to get the desired result


Here's where I'm stuck.
Column A, in the actual workbook, is the result of a formula so the blank cells are not actually empty.
To represent this, A5 in the sample is ="".

If A5 was actually empty, I would be able to use this:
=SUMPRODUCT((A3:A6)*(B3:B6=TRUE)*(D3:G6=TRUE)*(D2:G2))

I was able to get this working using a helper column but wanted to see if I can put it in a single formula.

That's it!

It transferred over to the main sheet as well.

Thanks Dave.