I can't see how that hooded system would work in a helmet. Coolshirt has a Cool-a-Clava that goes into a helmet. About $110.

However, my choice would be an integrated helmet. My choice would be the Roux composite or carbon helmets that have the cooling built in and their own dry break connector on the right side of the helmet. The helmet also comes with a drink tube, mike, and earpiece built with another quick release connector on the left and an air-port on the top. Not the least expensive helmet, but possibly the least expensive system. It includes its own emergency helmet removal system, but it is unlikely corner workers would be familiar with it.

I found the air is necessary to keep my glasses from fogging, especially during yellow flag laps and red flags on humid days and nights. Coolshirt also has a Dry-Cool Air System that adds a cooling tube with an integrated helmet blower. However, that is a pricey $590.

It is surprising there isn't a strap to ensure the clasps don't release in a crash.

 

Bolted to the floor.