Which way should my joists run for a tray ceiling?
If it was me, I'd do 30" joists... they math with less waste out of 8' sticks, and the structure will be more substantial if you walk on it in the attic. 

My only hesitation is about the light from above in the picture. Is there a chase for a skylight that you haven't mentioned? If so, design for that, rather than anything else.