Michael,
In Case 2, 4 BCQ pieces must be placed on 4 squares (c1, d1, e1, d2),
giving only 1 combination of filled squares. The same applies to Case 3.
Removing this factor of 4 reduces Case 2 to 72 combinations and Case 3 to
144, making the total number 864, which matches the figure I found by
counting in a somewhat different way.
Nova Chess features a great many unusual and interesting pieces, but the
pieces in any given set should be fairly easy to learn, and the game looks
quite playable. Nevertheless, it will be a while before I've played all
possible scenarios. ;)