Going from downdraft to overhead will greatly increase the effectiveness of your ventilation system, which counterbalances your worry of the duct turns reducing its effectiveness. Capture & containment are not at all as effective with downdraft. If the hood's blower is sized appropriately for the duct run, including the turns, it should be very effective.

Building codes generally don't allow you to have ducts that change direction. You either have to continuously go up or continuously go down with the slope of the duct. This helps with efficiency, but more importantly it's a safety feature that minimizes the risk of grease build-up that can result in fires. Some building departments are more relaxed about enforcing this aspect of the code. But that doesn't mean it isn't a good idea anyway.

You should probably plan to run new ducts when installing the overhead hood. And yes, overhead works so much better than downdraft. I'd always pick the former if I had the option. This is particularly true when using gas ranges, where the physics simply doesn't work in favor of downdrafts.

After you have figured out the how of the hood mount and ducting scheme, please review 'hood' and 'MUA' threads here to gain perspective on the what, i.e., the hood, duct, and blower parameters that you should meet along with the requisite make-up air system parameters, where applicable.

Thank you. Haven't heard of MUA, very interesting. I know we have a MUA system in our basement near our HVAC system. I haven't heard of it in a kitchen with an open floor plan

The idea of make-up air is that no air is pulled out of the kitchen via the hood that isn't replaced with low differential pressure between the house exterior and the kitchen. This requires either a very leaky house and low CFM kitchen hood, or a deliberate path that may or may not need a blower of its own.

Hence, MUA typically consists of a duct inlet, duct, filter, (optional* blower and optional silencer), damper (possibly controlled), heater (optional in mild climates), and a diffuser** to direct the MUA in a direction where it can approach the hood with minimal turbulence as well as not "short circuiting" the hood in its function of capturing and containing the rising cooking plumes.

Please read the first dozen or so pages of the Greenheck Guide at this link for understanding the basic concepts that residential kitchen ventilation attempts to approximate from the commercial world.

https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf

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*By optional blower is meant that to avoid back-drafting combustion appliances where present and not provided with their own MUA, a blower is needed to compensate for duct, filter, heater, diffuser, etc. pressure losses.

** See Hart and Cooley catalog to see the difference between the preferred diffuser vs. a typical register. Of course, if the MUA is introduced in another room, the means of introduction can be much more casual than when introduced into the kitchen. Kitchen hood measurement laboratories use perforated walls across the otherwise empty test room to introduce low turbulence MUA when appropriate.