Just checked Graeme's book:
The original pressure for the 3-inch .500 NE cordite 'factory-load' was 16 tons.

Using modern single-based powders, the same ballistics can usually be achieved with only 13 to 14 tons pressure.

Expect the extra 1/4-inch of case-length in the 3 1/4 version to be only slightly less, since with modern powders the problem is usually too much space in the case, which then requires a filler or wad-column.