I can’t comment on the technical side since it’s not my expertise - I’ll just say that based on your ceiling height I’d recommend a simpler hood design. No mantle. It’s overpowering and heavy with a lower ceiling.

Not to mention it’s off center with the ceiling detail which is another reason to downplay it and not accentuate it. This goes against your goals but I have to speak up.

How do the removable stainless baffles for trapping grease fit in your design?

this has technical issues beyond many of us . but if you can reduce the issues to primarily "centering" of stove, then measure what a swap of the two base cabinets left and right of range would do to help. Un-install counter.....swap those cabinets ….and proceed. If this achieves a solution for that.

The lowest wood piece of the hood needs to be at a minimum of 66"-72" AFF. Since your ceiling is only 84", you don't even have room for anything but a very slim profile stainless hood. A mantle hood does not begin to fit in 12"-18". It needs at least 24"H, and that is with a much smaller range. This will be badly out of scale. Plus are planning a fire hazard, with wood inside the prohibited zone for combustibles. Your insurance company will decline to pay for that fire claim.

"Is it safe to have the top of this arch 24" above the range top?"

Definitely NOT. 30"-36" above the cooking surface is the MINIMUM height for any wood above the cooking surface on a wood hood. Covering that wood with steel, drywall, or cement board, does not make any difference. Having wood anywhwre in that zone violates the clearances. The inspiration picture violates code.

You cannot do such a large arch - the overall height of this piece will be approx 18" ( 84 - 18 = 66 ) Do a 2" - 2 1/2" arch on the valance. If you do a column on each side you could then do a crown molding detail that will return on the column and not interfere with the doors of the cabinets. The opening underneath needs to be based on the actual exhaust unit that is required for your range - your appliance folks should be able to help you with that. It will be a challenge since you have a reduced ceiling height and you have an offset vent line ( which needs to be changed - in most areas flex duct is not allowed ).

You could also do a chimney style

Here are a couple of pictures for short mantles you could create

Good luck - I hope you can figure something out!

A lot of good advice above.

The first question is how functional you need this hood to be. If you don't cook in your kitchen and it is mainly for show then that's very different from if you actually use your kitchen and you need your hood to work properly.

Start here: https://www.gardenweb.com/discussions/5161173/hood-faq

For function, deeper is better so your husband's 24" is better than 22" but 27" or 30" is better than 24".

You'll want to use a stainless hood liner such as from Wolf or Braun or Modernaire or Captiveaire or whomever.

As @Kaseki mentioned, an inline or external blower will be much quieter than a blower in the hood itself. And IMPORTANTLY, you need to consider make up air.

Why is the stove so much higher than the counter top? Can you steal a few inches by removing, lowering the legs?

Hi all contributors, I know it's disappointing that the OP never got back to you or thanked you for all the wonderful advice, but I wanted to let you know that this thread popped up in searches for hoods for my own kitchen redo in January 2019 and has been hugely helpful. Thanks to everyone for the excellent advice, tips and links!