Advice on installing a ducted range hood?

Howdy makers and various DIYers. I’m doing a full-on gut renovation of my kitchen and I’d like some advice from anyone who feels qualified to have an opinion.

I’ll be installing a vented range hood over the gas stove and I think I have a couple options for the duct route. Hopefully my scribble drawings are illustrative enough to convey the ideas.

Here is the first option:

There is plumbing and other conduit in the soffit and I need to check that there is room up there for the duct. I’ve seen the inside of it briefly and I can’t remember. There is a tub/shower above it so going through to the roof just isn’t an option.

The second option:

The idea is to run the duct alongside the plumbing up there and vent it above the patio door. There is a false beam that covers that part of the ceiling. Aesthetically I’d prefer the vent to be on the side of the house as it would be in the first option, but I like the idea of being able to access the ductwork easily. Also potentially less drywall repair.

The decision will impact the logistics of the remodel, and I’m just not sure if one of these options is clearly better than the other.
Anyway- if anyone has advice/experience to share on installing a range hood I’d love to chat!

The two things i see potentially affecting the decision are the amount of available space in the soffit, and whether or not there is a load bearing beam over the patio door.

I have an inspection borescope that can look into the soffit with minimal drilling. Also I did find a small air compressor if you still want it.

Good call on the load bearing. I need to see if there is a route that could avoid that. Code dictates that I will likely need >6" duct to account for the elbow. I wouldn’t mind dropping the soffit to accommodate if needed. That would still leave room for the fridge, and I’m building open shelving on that wall so cabinets arent a concern.

I ended up just buying a compressor that I knew would work with the framing nailer. I think I can’t resist buying new tools… ┐⁠(⁠ ⁠∵⁠ ⁠)⁠┌

I would suggest putting your duct work in the existing soffit if at all possible.

I’m thinking I’ll actually end up running the ductwork along the underside of the soffit and just leave it exposed for now- it’s a little industrial but I think it will look nice if I paint it a hi-temp black.