With a strong prescription, the frame decides how thick the lens will be. A minus lens is thin in the middle and thick at the edge, so the further the edge from the centre, the thicker it gets.
Pick a smaller eye size and a frame that puts your pupils near the middle of each lens. That alone can save a few millimetres of edge.
Acetate hides a thick edge better than a thin metal rim. Round and soft square shapes spread the thickness evenly.
High-index lenses help, but they help most in the right frame. We will happily tell you when a frame you love is going to fight your prescription.