Gas range makers usually defer to local building codes when offering their fairly generic installation instructions. If this is a new installation into a kitchen without a previous gas appliance you might want to look into finding out if pulling permits for the work involved is necessary. Your local gas supplier and a local qualified gas fitter might also be of some help.

18" above the cooktop is usually what's required for flanking cabinets

I have a 36" BS range top with the 22k burners with a 36" VAH above and have had no issues in 8 years re: side clearance of the upper cabinets. That said, if I were to do it over again I would likely go with a 42" hood for extra side capture.

Looking at your hood choice, it does not have any "capture" capacity to speak of - the baffles are flush to the bottom. I'm sure that the hood will do a fine job in all but the most smokey of circumstances, but if you want improved venting then consider going with the 42" version of the hood (it only looks to be $100 more). That way you get both better venting and better clearance from the cabinets.

Of course, you then lose 6" of cabinet space so you'll have to figure if it is worth the tradeoff or not.

Good luck.

You need a 42" hood if you have a persnickety building code department and any light rail at all. And, it's better for the capture area. You need all the help you can get on that front with that hood since it only uses a 6" duct. The fan may be capable of the CFM it advertises, but choking it down to a 6" duct means that overall, you're gonna be limited to around 560-600 CFM max, which is borderline with that range. In your climate, you will also need to factor in makeup air and an ERV. That ups the costs of the associated components by quite a bit. Talk to a HVAC pro.