It would make navigating menu's feel a lot more accurate and intuitive for this kind of game. Is there a way to do this?

Go to the game's install folder (if you use GOG Galaxy, refer to the screenshot attached) and open the game.ini file with some text editor (e.g. Notepad).

Look for the following line:
GamePadDInput=0

and change it to:
GamePadDInput=1

This will disable the Analog Stick in exchange for the D-Pad.
For some reason, this also exchanges A with X and B with Y.
Fortunately, you can fix this. Look for the following line:

[gamepad]

Below that line, look for the following:

SELECT=5
CANCEL=6
OPTION=7
OPTION2=8

and replace them with these:

SELECT=7
CANCEL=8
OPTION=5
OPTION2=6