Blue Link mirror and handicapped placard

You just need a bit of patience to find the right spot. Once you find it, it is easily repeated.

I have a Sonata, but it is probably a similar situation. If you hold the card at about a 45 degree angle with the bottom towards the front of the car, you'll find there is a spot on the bracket where it easily slips over.

Other thoughts I had were to add a string and hook to the card, or add a hook to the mirror bracket, but once I found the right spot, it seems silly to bother.

As far as changing the mirror, I don't see that it is non-compliant with anything. You can just lay the placard on the dash, lean it against the window or a hundred other methods of making it visible. No law that I'm aware of says it must hang from the mirror, just that it must be visible. I've also seen them held onto the sun visor with rubber bands and when parked the visor is just flipped down into place.

I'd be inclined to try one of the 3M command adhesive hooks. The command strip is thicker so it can handled some curve. Alternative might be to stick it to the windshield behind the mirror.