A 363 is difficult to cool in low wind airflow conditions (woods racing) regardless of what radiator you have in the current market place. My question would be how are you getting the mud in the radiator? Is it from guys in front of you slinging mud? If so, you might consider making some mud deflectors with duct tape, plastic board, etc. Whatever you could come up with to keep mud from getting stuck in the radiator. If the mud is coming from large water crossings, that is a different story. There isn't much you can do about that to maintain radiator efficiency.If that is the problem, you really only have a couple options. Either decrease size of engine or increase cooling efficiency. Only 3 ways to improve the cooling efficiency situation: 1. reduce heat rejection requirement (reduce engine size) 2. increase airflow (either drive faster in wide open areas - not practical, or increase airflow by an external method -an electric fan) 3. Increase cooling capacity - larger radiator (unfortunately without good airflow, this doesn't accomplish much. Plus, you can space restrictions that really limits the amount of extra cooling you can obtain).
With all that said, that really only leaves you with the option to add a fan. I haven't really heard of anyone doing this with GREAT success, but there have been quite a few try. So someone may have done this successfully now. I'll leave you with 2 bits of hopefully helpful info. 1. If running one off of a battery is an option, that might be more feasible.
2. You may try contacting Michael Sytsma (he is on 250r for life facebook group). He makes custom electrical harnesses for a living. He has also made several custom electrical harnesses for our machines. Maybe he has got some ideas for you.