Engine bay cooling
I liked your idea to cut the cowl, but that being said, I'm not sure how well it would work. The cowl area at the base of the windshield is a high pressure area (thus how "cowl-induction" intakes work). The reason the C7 style vents work is the area just aft of the nose is a low pressure area. This essentially sucks the air out. I suspect the cowl area, being high pressure, would/could prevent air from escaping.. or perhaps even allow some back flow into the hood area, perhaps making the problem even worse!
Check out this CFD of a NASCAR, which shows the low pressure area roughly where the C7 vent would be, and the high pressure area at the base of the windshield.







