when moving a selected object using the up/down or left/right arrows on the keyboard, instead of "nudging" the object, the object is moved a long distance.

Oh, can you please share a short video for this? and confirm the following:

Please go to Illustrator > Preferences > General (Mac) or Edit > Preferences > General (Win) and check the Keyboard Increment value — when document units are set to inches, this value also reads in inches. Try setting it to 0.01in and see if that fixes the nudge behaviour.