CAKeyframeAnimation() configured for 'scrubbing', how to smooth transition to stop points?

Question

I'm animating an object (CAShapeLayer) along a bezier path by pausing the animation and setting the timeOffset manually, which moves it to fixed locations. But the movement is jerky. I want to be able to set the next offset and have it interpolate/animate smoothly from spot to spot. This is essentially what I'm doing. What should I do to smooth out the transitions?

    let bezierCurve = UIBezierPath(...)
    let shapeLayer = getShape()
    layer.speed = 0  // pause
    .
    .
    .
    let pathAnimation = CAKeyframeAnimation()
    pathAnimation.keyPath               = "position"
    pathAnimation.path                  = bezierCurve.cgPath
    pathAnimation.calculationMode       = .paced
    pathAnimation.fillMode              = .forwards
    pathAnimation.duration              = 1
    pathAnimation.isRemovedOnCompletion = false
    pathAnimation.beginTime             = CACurrentMediaTime()
    shapeLayer.add(pathAnimation, forKey: nil)
    layer.addSublayer(shapeLayer)
    .
    .
    layer.timeOffset = pathAnimation.beginTime + n  // note: periodically update n