I finally got around to checking the height of my Honda OEM 27" Bighorn 2.0s today. Pressure was down below 10psi in all tires, and height of the rear tires was 26.25". The front was 25.5". The owners manual says 14psi for the deluxe model, however the tires themselves are marked "not to exceed 36psi". I always felt that 14psi was a little soft for these 4ply tires (too much side wall roll), so I aired them all up to 20psi today, and checked tire height. The rears were at 27.25" and the fronts were 26.5". Seems like the tire height of the factory Bighorn 2.0s, is relatively true to nominal at 20psi, but they may grow some more after leaving at that pressure for a few days.
I'll check them again in a few days to see if they've grown any more, and report back. Hopefully this information will help people considering new tires to get a better feel for what sizes will fit on the stock machine.