Casual track days? You might skip the oil cooler, I did... 270ish isn't *that* hot
I do run 5W30 synthetic to get viscosity a smidge closer to nominal.
Or as someone else in one of these threads suggested, you could send a fresh sample of oil to Blackstone, then send another sample after tracking the car and see what they say about oil degradation and/or metallic particles. If oil isn't degrading and metal isn't being eroded beyond reasonable levels for your usage, why bother with an oil cooler?