I have read the thread with interest, if it was me I would approach it all from a very different angle, although a gas hob produces both waste produces and heat which need to be removed, an electric induction hob does not produce the waste produces, or the heat of a gas hob, but is as controllable unless silly touch controls are used, and a 3 kW induction hob is around twice as hot as a 5 kW gas hob simply as all heat goes into the pan, and not into the kitchen.
So maybe the way forward is to kick the gas to touch and move to electric induction then there is only a need to remove odours, which a charcoal can do, no need to extract to outside, and if you do extract to outside the rate can be much lower.
You would also at the same time get all the extra safety features, no naked flames, no combustion produces, auto overheat shut down, auto switch off when pan removed with permanent switch off if removed for long time, putting it in simple terms if some one invented a gas cooker today, it would be banned, it is only because of its historic use that it is still allowed. The whole idea of balancing a pan on fingers rather than on a flat surface seems daft.
Pre induction hob I can see why people used gas, but today gas is just a cheap way to have a controllable hob when you can't afford an induction hob, and with the cost of installing an extractor, likely induction is in your case the cheap option. Just be aware that touch controls can spoil an induction hob, with knobs it is as controllable as gas, but depending how set up, with touch controls it can spoil the induction hob as it takes so long to adjust heat settings.