After
Logitech buy
Saitek they alleged improved QC, but complains still, specially about potentiometer in secondary axes (rudder, throttle, rotaries).
Anyway get
Logitech G X-52 PRO that have some improvements over X-52 "vanilla" cost more but still in your budget.
Unfortunately, up to $200 no more options in
HOTAS other than Thrustmaster FCS
HOTAS, that cost less, but their T.16000M FCS stick is just a "toy'ist" 4 buttons + POV HAT grip.