Haven't been for a couple of years, but have parked by lake no probs, don't know about visitor centre car park. The road even is quiet at night.
For very wild, look just a little further north for Llyn Aled Isaf, it's a reservoir and there are a few places, especially at the north end of the lake to stay, very quiet, virtually no light, gets all the wind, rain and snow etc, but truly wild. Lots of walking around the moors.
Don't park in the passing bays or at the entrance to fields etc it's a single track road.
Wild & beautiful.
Pete