On the sending end, the transmitter will almost certainly have a simple potentiometer connected to the joystick, or a switch connecting one of two resistance values for a switched input.
I would have thought it would be easy enough to replace this with an Arduino-controlled driver circuit that switched between two alternate resistance paths depending whether an Arduino output was high or low.
On the receiving side there is already a servo input library which can interpret the PWM signal output by an RC receiver and return the corresponding 'servo position' value.
To use these as a comms link, you would need a library similar to SoftSerial on the sending side which output the bit stream as a sequence of high/low values on the pin that controlled the transmitter. On the receiving side you would need something similar to poll the 'servo position' and convert this to a sequence of high/low values which were then passed to a modified SoftSerial library that interpreted it as a serial stream.
You would need the bit rate to be substantially slower than the RC frame rate - which would usually be 50Hz. It may need some modification to the SoftSerial library to enable it to cope with baud rates this low. It would be prudent to include parity and sufficient stop bits to enable reliable synchronisation.
Note this is one-way only - there is no return path.