I thought I'd try the analogmouse program from Aminet that would allow you to control the mouse with the analog joystick.

AnalogMouse.lha 1.0 util/mouse 1521 12K 1998-03-19 m68k-amigaos Use analog joystick as a mouse. - (readme)

However, it doesn't work properly unless you give it pot values from 0-127. 128 and above causes a rollover in how it computes things.


AnalogMouse v1.0 by Piotr Pawlow (PP/UNION)

1. Introduction

AnalogMouse is a CLI-only tool that allows you to control your
mouse with an analog joystick connected to the joystick port. You can use
your joystick to work with the system as well as play many mouse-only
games. I tried it with DoomAttack, ADoom and MegaBall and it was working
very well. (To be honest - I made this program just to be able to play
DoomAttack with my analog joystick, compatibility with the system and other
games is simply a side-effect smile

3. Requirements

Any Amiga with at least Kickstart 2.0, about 8KB of free memory
and 6KB of free disk space. (or at least Pentium Pro 200 with a huge
hard drive and a lot of memory, running UAE smile

4. Quick start

Just run it. That's all smile No calibration is needed, you don't
need to set thousands of options, install a special Plug'n'Pray Advanced
32-bit Analog Joystick Driver(tm) and stuff...
After starting AnalogMouse move your joystick in all directions so
the program can find minimum and maximum values and aspect ratio of your
joystick. Then move the joystick to a neutral position. If the mouse
pointer still moves, correct it with TRIM potentiometers.
Press Ctrl-C to exit the program.

Feeding it values from 0 to 119: (the 4682 stuff is because I've mapped the analog joystick to the keypad keys)

Sensitivity 10 makes it a lot easier to control.

[Linked Image from i.imgur.com]

Feeding values from 0 to 128 causes a rollover and the mouse becomes uncontrollable:
[Linked Image from i.imgur.com]