Trying to calibrate the joystick never works - circling leads to it always being way, way off. Any idea how to set up a DS4 with Jazz?

Try this to get the D-Pad working: https://www.gog.com/forum/jazz_jackrabbit/controller_support/post4

Unfortunately, this disables the analogue sticks altogether.

note: I can confirm this works with a PS3 (Dualshock 3) pad emulating a 360 pad. I'm assuming it would work with a PS4 pad, but can't confirm.

Antimicro running in the background is my go-to solution for controller issues. lol @ the suckers who paid for xpadder.

In DOSBox, it's usually better to set up the game for keyboard controls and then use programs like joy2key to map joystick buttons to keyboard mappings expected by the game in question. The DOS games, except for few very specific cases, such as flight simulators didn't support analog controls anyway.

This also would solve the d-pad issue you're having as well, since you can map d-pad to keyboard keys with joy2key.

Happy hopping on holidays!

For Mac users with macOS Ventura ver. 13.X.X running on an M-series processor-

https://youtu.be/bylk5VRlJPE