I think I have a cheap way to introduce fresh air right into fan. I've worried that the holes in the nose will not be able to flow enough cooling air. I found this vent unit at Home Depot with a 4" pipe--about 10 bucks. I believe with a bit of trimming it can be inserted into a DIY 4" hole in the pan and the tube is the right length to reach directly over to the fan. The tube should clear under the exhaust. My vent came in brown but flat black plastic aerosol paint should cure that. When I have it trimmed, painted and installed I'll show photos and tell you how to do it.
We are now fulfilling hood kits orders at the rate of about two to three per week so that part is working.