jct32:
What would you recommend doing instead of this?
As I said above:
Rather than (or in addition to) the joystick value, I would want to see the servo command value servoValX.
So print out the result of the analogRead, value1.
AND print out the result of the map function, servoValX.
Move your joystick to the limits of its movement, noting the highest and lowest values that the analogRead brings back. Also note how close to 0 and 180 servoValX gets.
If you get 0 and 1023 for the limits of the joystick, you are good. If you get different numbers, put those in to the map command where you currently have 0 and 1023.
Then try again. How close is servoValX coming to 0 and 180 now?