How can I draw a UIBezierPath onto Google Maps using the iOS SDK?

Question

I have created a curved UIBezierPath from a list of points on the Google Map in my iOS application. Is there any way for me to draw this path on the GMSMapView? The only options I have seen so far for GMSOverlays are straight lines (GMSPolyLine, GMSPolygon, etc).

I have a workaround in which I create a CAShapeLayer from the UIBezierPath, and add it as a sub layer to the GMSMapView, however my path then runs on top of the GMSMarkers on my map, and I need the markers to show on top of the path. If there is a way to modify this workaround to get the path underneath the markers that would also be acceptable.