Alright I'm going to throw whatever reputation I have on the line here. And yes this is a serious question.
Apologies for the shoddy imagery. I had a couple ideas to get the Brownian Ratchet to work. I know that the Second Law of Thermodynamics says such things are impossible. But as far as I understand it the second law is there not because of some hard mathematical argument but as an underlying axiom. Mostly because its obviously true in almost every theoretical and practical experiment you can imagine. Then we come up with oddballs like the Brownian Ratchet and it gets murky.
So I had two ideas for getting our ratchet to work. Now I haven't read up on the argument Feynman gives directly. From what I gather from around Stack-exchange and Wikipedia there are two immediate issues.
The first is that that pawl has a lot of energy and jiggles with its heat. Occasionally it slips and any of these random time events can be modeled as uniform pressure in the long run instead of the Brownian motion they are, since it all evens out anyway.
This seems like a logical argument until you consider the effect of torque. If the heat energy is everywhere equal then if you make the paddle large enough, but still light enough to turn, then the force exerted on the outer edge should exceed the force from heat on the pawl.
This is the same principle we use everywhere in gears and levers. It takes less force to move but a larger distance and a larger time. Since the required force to accomplish the turn in one direction is not the same as to go in reverse you should have net energy over large spans of time.
Besides the large paddle, small pawl idea I also considered getting rid of the problematic pawl for a design that was unidirectional. Asymmetrical gears I've heard were suggested at one point. I personally have considered a complicated “caterpillar ratchet” that grips on and moves around the ratchet inchworm style and a simpler “spider” ratchet. The spider one has a track that a set of teeth mesh with. The teeth are like leaf springs that can handle a compressive load. They push up against the outer wall and are prevented from rolling backward both by this compression as well as a staggered set of teeth that are offset.
Now the reason for the staggered set of teeth is not immediately obvious. If you have a single set of symmetric teeth then much like a single pawl there is a moment when the position allows one to slide backwards. If improbably it tried to move backwards at the speed of sound it could make more than a full revolution in reverse with a symmetric or pawl setup. With an offset set of teeth there will always be a tooth in contact with the lock. You will get at most a half-tooth reversal.
Now our random jitters should supply an equally lucky reversal for each forward jolt we experience. Except the probabilities are different because the teeth cater to their own statistics. The forward motion is a long-drawn-out process by virtue of the large paddle and torque trade-off. You take the same energy (thermodynamic equilibrium) over a longer period of time than the short jolts required to move backwards. Since no matter how powerful the jolt it can only slip a half-tooth back there will be a paddle size where the frequency trade off that favors the larger slower paddle.
Also, I could be wrong but thermodynamic equilibrium means "even temperature" and does not imply the same pressure across the system. Couldn't you manipulate a pressure gradient to your advantage?