Get a realm overhead hood, with some capture area. Not the expensive and useless lies.

Look at the retractable hoods

Induction for your hob will help. That method reduces some of the ventilation requirement by eliminating the waste heat from gas. Best Cattura is a downdraft vent that works better with induction. No flame to be affected. It will not be near as good a properly sized overhead. On a peninsula an overhead is also less effective than when you have a wall behind the hob. Then you can consider makeup air. Here's the marketing viewpoint.

thanks @Patricia Colwell Consulting I didn't even consider those.

@dan1888 we are going with an induction hob. I will have a look at this thank you

My Wolf Pro Island hood base is mounted 34.5 inches above the counter. This is equivalent to about 1.8m above the floor. The top of the hood, which is 18 inches (0.46m) is thus 2.24m above the floor. This plus a surround of sorts about the duct would fit under your ceiling, or you could raise the hood to be flush with the ceiling giving you a hood base a bit over 3 ft above the counter. Download the Wolf Design Guide from the SubZero/Wolf web site for dimensional parameters.

P.S. The cylindrical retractable hood shown above will have poor capture performance against higher velocity plumes. It needs some sort of inverted tray type attachment at the bottom that overlaps the cooktop by a few inches in all directions.

"Most recommend a distance between the hob and extractor around 500-600mm."

I don't know Mr. Most, but 30 - 36 inches (760 - 910 mm) is appropriate for properly overlapping residential canopy hoods, 48 inches for commercial hoods. Undersize, underpowered hoods may need to be closer, but they will only capture and contain from the rear burners/hobs.