Not an electrician: I believe the NEC prohibits using ducting as a wireway (conduit) because it is not approved for the application. There are also requirements on cables and conduit when in an air plenum, such as a ceiling used as an air plenum. Truly abandoned ducting is just metal surrounding a cable or conduit run. If the duct is greasy, then any conduit in the abandoned ducting should be sealed, and in my view incapable of supporting a fire, such as thinwall, IMC, or rigid. Flex might allow grease to intrude upon the conductors. UG cable might be OK. PVC conduit might be allowed. I have never noticed this particular case addressed in the NEC.

For electrical questions, I argue that it is better to ask permission than forgiveness. See your Code Enforcement officer for advice. You may have to tear out some part of the ducting at each end for it to qualify as abandoned.

I think it is a good idea, pending approval, if the duct is buried and the path needed is otherwise inaccessible without trenching under the building.

Duct is buried in slab. I think your ideas on making inaccessible are wise...one electrician said no way. The other suggested..

Switching to induction will likely have no effect on your asthma. You are likely dealing mostly with the byproducts of cooking itself, not gas combustion (as well as other things in your home).

You need proper ventilation for whatever range you have (https://bamasotan.us/range-exhaust-hood-faq/) as well as proper ventilation and filtration for your home.

You could use the existing circuit and avoid using too many burners on high power at the same time.