Now from what I've managed to gather from bits I've read, it's only possible to control 2x PWM fans at 25mHz with a single Arduino Uno, so I'm imagining to do this I'd need 3 Unos? One for each pair of fans, then an overall arduino which controls the final fan as well as the two screens and reads the temperature sensors and potentiometers.
One Mega2560 should be enough to control at least 8 fans.
If I understood your description correctly you need to control only 3 PWM signals, an UNO should be able to handle that. If you take I2C LCD moduls the rest should be no problem too.