I solved my recent post regarding kitchen sink depth vs drain height, but barely. In my case, I had a dishwasher fitting above the p-trap, which used up about 4" in height. What if.... you have a 90 elbow coming off the drain basket and a short pipe leading into the dishwasher T and then into the P-trap? the dishwasher hose would come down from the top, and the T would slant towards the P-trap. It would save you a couple of precious inches. Would it drain into the trap or back up into the sink?