This joy & throttle combo need a USB controller with at least 5 axis: 2 for joy X, Y, 1 for throttle, 1 anthena, 1 for range.

Or 7 if you plan use a PS2 mini-stick (2 axis) for replace the "IBM" mouse under thumb in throttle leaving the TQS like Cougar TQS.

For the 1st case the Arduino PRO Micro is sufficient, for the 2nd you need a board that allow more axes input (PRO Micro is limited to 6), e.g. Teensy 2.0.

Or use one PRO Micro inside the joy and one inside the TQS, leaving the controllers independent. Samples: http://forums.eagle.ru/showpost.php?p=2725761&postcount=4

Firmware is MMjoy2 - link for the last revision available in first topic of this thread.

Read two post above your the inconvenient of A1302 HALL sensor.

The only part of original electronics that you will reuse is the Shift Register board inside F22 grip.
Remove the other circuit boards but leave buttons, HAT, wires and his connector in place.

TLE5010 is contactless sensor (for automotive industry), in practical terms work in joystick similar to HALL sensor, reading a magnet field, but is more easy to setup. Need assembly in small PCB with resistors and capacitors.

Sample, installed in Cougar TQS: http://forum.il2sturmovik.ru/topic/3027-mmjoy2-i-thrustmaster/page-2#entry322826