For 8 cores?
Is the CPU overclocked or do you plan to overclock it?
If so, I would switch to an AiO/all-in-one water cooling system.
https://www.digitec.ch/de... No more than 240mm!
Air and water both have advantages, but the reason I chose water for mine is also because of radiator height and weight, which pulls on the MB.
But if you want air, you need something strong, so maybe the big brother of the NH-U12S:
Noctua NH-D14 (16cm) it is "only" 16cm high, but still has the weight of a baby with 1240g.