Hi Hunterdude . . .
Is the engine apart? Specifically, is the head off? If so you can calculate the C/R by measuring the volume of the combustion chambers and comparing it to the displaced volume.
In performing these measurements some details specific to the build need to be taken into consideration. First, has shortblock been zero decked? If the pistons are flush to the deck surface at TDC then the answer is yes - and therefore the very top of the cylinder need not be added to the combustion chamber volume. If the pistons stop short of the deck - the volume of this shallow cylinder needs to be added to the combustion chamber volume.
What head gasket will you be running and what is it's compressed thickness? The same shallow cylinder volume estimate applies here as well.
AFAIK the 477 is the most abundant head in terms of production volumes on the civilian side - which is why whoever assembled your engine may have chosen it in order to move ahead. If the head was milled the volume (compared to stock) may be considerably less.
Back to the original questions - if the head is off you can take a graduated cylinder and fill it with mineral oil to a round measurement mark on the graduations. Then set the head upside down on your bench with wood blocks/shims to level it in all directions. Pour the mineral oil into one of the combustion chambers until level to the top. The remainder in the graduated cylinder will reveal the combustion chamber volume.
I'd measure what's in hand before shopping for parts.
regards,
stock49