The issue is that when I plug it into a joystick testing program, the new pots are kind of "off center", I guess is the correct way to describe it.

The joystick decides what "center" is when you first plug it in. This is the "0" point on the potentiometer. If the joystick is "relaxed" when you plug it in (its springs have it sitting at its center point) then theoretically you should have full range of values in the computer readout. But that's not what's happening. When I plug it into the computer, it shows these values with the new pots:

X-axis, stick full leftwards: -32768
X-axis, stick full rightwards: 30711 (or a bit higher if I push really hard)
Y-axis, stick full backwards: 32767
Y-axis, stick full forwards: -31226 (or a bit higher if I push really hard)

Whereas the original potentiometers give me full range -32768 through 32767 for both axes.

Seems "OK" in-game so I'm not "too" worried about it. I just wonder if I'm not getting my full turning rate in my X-Wing when I'm banking right or diving. The way this thing is constructed, there's no way to "adjust" the pot positions, it's all plastic snap-in-place stuff and the shafts of the pots are D-keyed.