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

Here’s a suggestion: http://www.suncoastsheetmetal.com.au/cms/index.php/domestic/kitchens.html

Does anyone know a place in Melbourne that can make a decorative country rangehood for a 10 ft ceiling

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