Here is the gist of a reply I got from XFX:
"...
The reason DXdiag shows incorrect memory is because the program hasnt
been updated to be 64bit. Its 32bit. That means the program can only read a maximum of 4096mb of memory
(
http://www.ehow.com/info_8405314_define-32bit-operating-system.html ) . On the DXDiag report display memory
normally equals `Dedicated memory + Shared memory`. Dedicated memory is the memory on the card (so this is indeed
being reported correctly), shared memory is the amount of ram windows allows the card to access. Add those together
and you get total display memory. Since your two values are at 3043 and 1787, your total video memory is actually
4830mb. Since the max DXdiag can read is 4096 you only see whats left. 4830 - 4096 = 734 . An easy thing you can
do to see what I am talking about is to get your memory to 4gb or less. So remove all sticks of memory but 2x2gb stick.
Then check the DX diag results. It should be something like 3800mb of display memory
..."
While his subtraction is accurate, this explanation fails to account for the correct readings you and others get from DxDiag.

It also fails to address the out-of-memory issues I have in Aces High.
*sigh*