I am doing what I call a 'sandwich' mount, which invloves dropping the sink into one thickness unfinished mdf board, securing it in the typical drop-in fashion, then making my own faux stone finish from epoxy on another thickness, making just a slight alteration the mdf where the top layer will sit on the sink rim (1/4 inch higher). This will allow me to 'pour over' the edges with the epoxy on my top layer, giving it a proper finished edge where in the interior rim. Once in place, I will screw the two mdf layers together from below. Also, the bottom layer is cut to FLUSH with the cabinet fronts, and the top layer will have an additional strip of mdf running under any front edges to give me a full thickness of finished, poured-over front edge. So simple,tons of fun making this epoxy counter, and we can use any sink we want. You can only 'sandwich mount' if you are making your own counter, though. And soooo much cheaper and better than the big stores' cheapest laminate or solid-surface counter. My whole kitchen, including an island, is costing me less than $500 including mdf, epoxy and supplies, and the sink.
I came up with this when I realized that drop-in sinks and undermount sinks have more in common than differences. They all have a nice flat rim top, maybe just 1/4 inch more narrow a rim than undermount sinks.
Contact me for pics of this process if I didn't explain it sufficiently.