What you could do there is put it in the keyboard so that about 1 centimetre worth of edge is accessible, with the rest under whatever else you've got in there. You'd have to test with your ring to figure exactly how/where you're consistently triggering, with the v3 unit I get good reads from the side within 4mm, following the direction of the antenna loop at up to 10mm and over the center of the board for slightly more distance in the right orientation.
You could also play around with disabling the integral antenna and using your own loop antenna with it.