Arduino Pro Mini + Xbox 360 USB gamepad + RN-42 Bluetooth – how many buttons max

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.