--Under acceleration it sometimes feels like there is no power, other times like there's a full 350hp

That one sounds very I/C pump related. This is because your heat exchanger still cools water even if the pump isn't working, so when you're moving and air is going through the heat exchanger then it can usually cool the water and therefore the supercharger enough to lower the intake air temps back down enough to turn the supercharger clutch back on, temporarily.