I’ve personally seen to many fan clutches take flight into radiators to suggest ever using them on anything that revs rapidly.
That being my opinion, if you choose to run one, what you’ve read is correct. Any shrouded fan will move more air with the blade tips out of the enclosure. I doubt that is the issue... but it is true.
First thing I would check is if it’s working. A lot of them have adjustable thermostats. See if the fan is moving hot air.
I’ve also noticed that many temp problems can be fixed with correct ignition curves.