I looked into RN-42 module manual and does Bluetooth HID really limit joypad and gamepad modes to 16 buttons max? All gamepad/joystick reports need to be 6 bytes long, two of which are a bitwise mask of the current buttons state. This leaves us with 16 buttons max as far as I understand.
I'm trying to add additional buttons to my xbox-360 gamepad and bluetoothify it, but it already has 16 buttons as it is (14 if you count triggers as z-axis, which incidentally I also don't really know how to fit into the RN-42 report, unless I were to just send them as digital values and not analog). I know USB HID protocol itself allows for way more gamepad buttons and RN-42 doesn't have problems handling keyboards with much more keys so it'd be weird if bluetooth HID protocol just limits gamepad to 16 for whatever reason.
It's the HID report descriptor that limits the number of buttons and axes you can send. Bluetooth HID will let you send whatever you want if you provide your own descriptor, but the RN-42's built-in gamepad mode is configured for 16 buttons and 4 axes.
I don't think the RN-42 will allow you to specify a custom report descriptor, but maybe there's a way to at least add some buttons. The manual describes a "combo" mode for sending both keyboard and mouse codes, and also mentions that you can send 16 additional HID Consumer key codes in the combo and keyboard modes. Maybe you could send those codes in gamepad mode as well? It would be interesting to dump the HID descriptors in each of the RN-42's HID modes to see which reports can be sent.