It sounds like the reader coil in the security system is tiny and behind thin plastic, which doesn’t couple well with the LF side of the NExT. What you’re doing with the diagnostic card (which is super clever, btw) is introducing a patch antenna that resonates at the same frequency, and changes the shape/size of the field so that it can couple with the NExT. That’s good news, because it means the reader is putting out enough juice, it’s just not shaped to couple well to the implant. I would try even more orientations of your hand and see if you can get it without the diagnostic card. If not, maybe pop off the faceplate and post a picture of the coil(s).
Check out this thread: