This MIGHT help... just a bit.
Many, many.... many years ago, in my hot rod days, I got the bright idea to shoehorn a 427 into a '37 Chevy's engine bay. Needless to say, there wasn't much wiggle room in the compartment... and because I'd had to use tubular headers to make it fit, under hood temperatures were a wee bit excessive.
I wanted to retain the hood sides, as if I could keep a Rat Motor a secret, and as a consequence of being enclosed, vapor lock was a constant source of "amusement". Even adding a cool can for the fuel line to pass through, provided limited relief.
What I did to pull the hot air out of the engine bay was pick up a couple of heavy duty, 12v blowers, set them up to pull air out of the engine bay and ran some metal flex tubing out, towards the rear of the car. I installed a switch so I could turn them on and off.
Surprisingly, they actually worked well enough to keep the fuel from boiling in the float bowls of the carbs.
I don't know if such an arraignment would make enough of a difference to reduce radiant heat from coming through a doghouse, but it might be worth a try. Perhaps you could use a pair of high flow bilge blowers, available through a marine supply house.