"Do we feel centrifugal force on a roundabout because it's spinning relative to loads of massive material in the universe? And it would be equally valid to say that other stuff is spinning while we're standing still?"
Could it not be argued that on the roundabout we know we are moving because we have experienced acceleration, whereas the world around us has not. I have never been very happy with that reasoning when applied to the twin paradox, so I would be interested to see someone shoot it down.

There never was nothing.