You can get slim range hoods that generally fit into the wall cabinets ours were approx 40cm deep which housed the complete operation, our plumber ran a 6 or so inch flexable ducting into the roof cavity and out under the eaves. Most brands make these. A photo would be helpful. https://www.thegoodguys.com.au/omega-52cm-undermount-rangehood-oru50x?CAWELAID=620013790000422290&CAGPSPN=pla&CAAGID=21711678566&CATCI=pla-376401441757&gclid=CjwKCAjw0qLOBRBUEiwAMG5xMNN63iJr0n0Bnxf31-Gt0t5s0vERt_lOwOYkC6uzovf9TDWwawry9RoCgxQQAvD_BwE&gclsrc=aw.ds&dclid=CLOv9erawdYCFc0slgodE5oLHg Where we didn't have wall cabinets we had tall boxes of stainless look laminate built up to the ceiling which contained the extraction unit, which was approx 30-40cm's and extraction ducting cheers

You have posted on the Australian houzz site. We may not have the answers your after.

Hello 61karwin, I do not have a range hood just an exhaust fan. I do not do much in the way of frying, I am however rather good at 'carbon' but find with a good breeze thru from open windows that it is no problem. The fan does need cleaning every now and then but I get a tall person to assist: a young one who is happy to get onto the bench! I do not see a problem unless your home is not well vented and you like cooking hot chips! Cheers Margot

For the small amount of range hood that would be in contact with the undulating subway tiles, I do not see a problem.