I might go a step beyond this and get a new 2.4GHz Tx module and add that to the joystick to make it a transmitter.
Fly-Dream make an affordable and reliable 2.4GHz DIY module with three pins for GND,+,PPM in.
I've been able to generate PPM from an Arduino in the past so now it's a matter of hooking the pots in the joystick to the analog pins and the buttons to the digital pins. The pots move over a portion of the total travel in a joystick so my Vref will need to be a bit above the max voltage the pot will register. So if the pot only travels between 0 to half way and I feed the pot +5v then the max output voltage will be 2.5V.
I've also ordered an 8ch 12bit ADC I2C breakout which samples at about 12KHz. This will give me more leg room at reading resolution of 4095. The high resolution reading then goes through expo / trim / end point / sample filtering maths and comes out at a resolution of 1024 per channel. As far as I can tell the PPM output resolution does not need to be any higher than that, nor do I think the timing in an Arduino can get any better than that.
The hat switch can be coded to move the camera tilt servo. Might even pop out the digital hat switch and put a Wii joystick in there for tilt rate control.
With the 8 or more buttons on the joystick I should be able to code it to give me all the PWM levels needed for channel 6 modes on the Arducopter.