study the doors again, they're not quite "flat metal all the way down", aside from the rumpled pattern below and the ridges on the cover plate, there's the handles to consider, they're quite flush with the existing metal, adding upholstery will need to accommodate all that .... and there doesn't need to be any sewing, contact cement works well, or you might get the shop to make up the fabric cover and work out gluing it on some mounting board yourself
Bill
