bump

I suggest you post this question on the Appliances Forum as those folks are informed on the fine points of ducting for vent hoods. Include the photos you have posted here. They need the following information:
1. Brand of vent hood insert, single or dual blowers re: cfm, also planned duct size.
2. Number of feet of duct run, number of feet from one transition to the next, and degree of angle for transition (i.e.,45 degrees/ 90 degrees?).
Could you build-up your crown molding higher to hide the ducting if it runs across the top of your cabinet? In my opinion, your ceiling vault is so high that running the duct straight up would be aesthetically unpleasing. However, going the alternate route, you would need to limit yourself to no more than a total of 3 transitions, each at least 24" apart, as these are the recommended parameters per my reading. I am struggling with an issue similar to yours, small kitchen, trying to avoid going vertical as an open ceiling vault is above my cabinets as well. Fortunately, though, my ceiling is much lower than yours, and my stacked crown molding is 6" high.