Sink drain with insufficient slope

My wife and I expanded our kitchen a couple of years ago. The general was responsible for the rough and I did the finish, which included connecting the sink drain to the drain pipe. The problem I ran into was that we put in a deep sink and the plumber left the drain pipe so high that I ended up putting in a section of pipe just before the P-trap that's almost level. This 6-8 inch section has gotten completely clogged after two years, I'm guessing because there's not enough flow.

Short of ripping out the sink and putting in a shallower one, or opening up the wall behind the cabinets to modify the drain pipe, is there anything I can do to improve this?

Thanks in advance,

K-

drain

What does "almost level" mean. Even exactly level would not normally cause a problem in that short piece, so you may have a different problem than you think you do.