Interesting question!
I dont think recirculation is a solution. Brake fluid is not like oil or coolant. It doesn't really flow anywhere as you mentioned.
I found this for dirt bikes:
Seems like what you were thinking about. The only issue is that it needs to be close to the caliper to be very effective and thats probably not possible on a car. Mounted further away would still cool the fluid, but that fluid would never see the caliper.
I think a duct to to cool the rotor is the best solution. Cooler rotor=cooler caliper=cooler fluid
I'm curious why you've dismissed that option.