Next part to get converted to I2C was the joystick module. This time I needed to use an ATTiny84 because I needed 2 pins for X and Y, 1 pin for the button and 1 pin for the LED plus 2 for I2C which means there are not enough pins available in the ATTiny85.
Soldering was a little easier because there are not so many connections required.
I also cut down the size of the module so that I could build 2 and put one either side of the main remote. This makes it a more compact unit.
The obligatory video below shows it working.