Wow, this is an excellent thread with lots of idea's and possible solution's. Great stuff!!!
One transmission cooling idea I had was maybe running some sort of ram-air/air-duct system underneath the VX that would channel frontal cold-air to blow alongside the transmission housing itself to help dissipate heat. Much like how NASCAR uses a ram-air ducting system to blow cold air on their brake's. I think something simular could be custom rigged to blow cold air alongside the transmission housing and the air ducting could even be routed directly "above" the KILBY's skidplate level.
The ram-air cooling effect would not be as radical as a dedicated in-line transmission cooler; and would only be operational at sustained forward speed, thereby keeping the temperature of the trans fluid within normal operating range. Just a thought.
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