Volfy,
Burt Rutan is unconventional, yet had to abide the laws of nature in his design. He has a very good understanding of these laws. He is a very able bodied designer, making good use of all possibilities offered to him.
Not everything unconvential works by law however, so that is not a discussion item. Only ignorants walk that road, until they know better.

Please check your fluid laws:
Boyle; P/V=C (used for static gas, non-adiabatic, so T=C) (V=volume)
Boyle-GuyLussac; P/(VxT)=C (if we consider the flow in the cowl low enough to be static)
Bernoulli; P x v=C (used for dynamic flow, considered adiabatic) (v=speed) You should have used Bernoulli and Boyle-GuyLussac.
Using these, you also will notice, that heating the gas either increases pressure without slowing down the gas, or makes the gas move faster because of their increased Volume and constant pressure, like in cooler ducts or jet engines.
The heating up of the exiting gas by the exhaust pipes will increase the pressure inside the cowl, because the pressure where the cowl flow merges with the outside flow is the same for both, and the larger pressure difference between start and end of the duct.
Thus the KR2S design effectively reduces cooling flow through the cowling, because there is less pressure difference left to sustain the coolant flow.