I think there is such a solution, in the form of a water ballasted boat design that I started working on in my spare time some fifteen years ago. The boat I'm building currently to test my theories is 33 feet long overall, 8.5 feet at the beam and draws 3.7 feet, including about one foot for its keel, which is about three quarters full. Her projected weights are about 6000 pounds dry and 14,800 pounds displaced.
Construction is dual chine, using plywood panel bent over standing main bulkheads.
All parts of the hull, deck and cabin are glued together with epoxy and the entire outside is glassed. Bits and Pieces in Plan and Top views, with summary specifications I first described this project in a September 1996 article for Practical Sailor magazine. Bits and Pieces hasn't been tested yet, but we have tested the UWB concept, at least in a half scale version. Her weights are about 800 pounds dry and 1,600 pounds displaced. To thoroughly test her seaworthiness, we purposely overpowered her with a 22 foot mast and sails from a Roberts 19.