Hmmmm.....
Somewhere I am not following your math. Is that 4 holes 2" deep by .875" diameter.
Think rectangular cavity....actually 3 holes, 7/8" diam, 4" deep with webbing removed between the holes and corners squared up. My math is on the mock up; a rectangular block, 2.5" wide x 4" long x 7/8" thick, equals 8.75 cubic inches, I hope

....a bit larger all aound than a deck of cards.
Real world, the bottom hole would be smaller and angled up parallel to the belly line. Not a rectangular cavity, but even larger volume if need be.