On my boat there are handles like this, with an ellipse grip, but your acrylic has a round indentation.
My acrylic was broken, and the service technician ordered a new one, the new one comes without handles, since the handles are glued, they literally tore them off from old acrylic, after removal, very hard glue remains on the handles, and because of this, the handles cannot fit into the indentation on the acrylic, because of this, service technicians drill the acrylic and put a longer screw to hold it. The problem is that then the base of the handle starts to turn and eventually screw off. I finally took off the handle, sanded off the glue so it could fit into the indentation, apply some epoxy glue, but also returned the screw, because there is a hole in the acrylic.
I think you will have to replace either the handles or the acrylic, in order to graze each other. You can try grinding the base of the handle so that it fits into the indentation in the acrylic, and then glue with epoxy and put the screw back. It is important to put butyl or some sealant around the screw. There are two places where water can enter, around the screw (a small amount) or if the handle does not tighten gasket enough, between the gasket and the frame (probably more water).
Mario