Hmmm...
I don't think I've had a car stop while in the round-a-bout.
One that I regularly do a left hand turn in... 2 lane ==> 1 lane ==> cross 2 lane and out, I watch the cross traffic very closely that is supposed to stop. Just to make sure they actually stop (probably had 1 or 2 that went through too close for comfort).
I think your problem was that you were trying to adjust your speed to just pull right behind a car, rather than clearly slowing to allow the car to pass, then going again.
A couple of round-a-bouts have a speed limit of 20 MPH, which is my target speed (more difficult for bikes than cars).