Have you considered using security screws that require a specially paired wrench to remove, instead of common screws, bolts, and nuts? It wouldn't take any extra space, and would make it very difficult for the wearer to remove the DL without permission.
One problem with security screws is that reasonably priced ones don't provide much security. Thanks to the internet, it is now easy to obtain drivers for the common screws such as the "torx with a button" screws. Here is an alternative idea -- although it will probably have to wait until Version 2. Make the receiver sense when the case is open. There are many ways to do it: the two halves of the case perhaps pinch a switch; or perhaps there is a photoresistor in the case that senses light. When the case is opened, the receiver "panics" and zaps like crazy. If the battery is internally mounted with several screws, then this will cause an uncomfortable delay between opening the outer shell of the receiver and removing the battery. This feature would not drive up the price too much, assuming there is a smidge more room on the PC board and room in the microcontroller.
Obviously this does not provide much security either, but it would discourage the wearer from tampering.