Had a similar issue with my kidzplay racingwheel.
For that i just mapped the analog control as D-pad without using the "Analog to Digital" option for the individual games i used it with.

Since your controller is broader, you can save the button mapping for entire systems, that do not use analog buttons at all.
Only the systems that do use it you'd still have to do it per game for.

Not really a solution, but its a workable workaround.

@dankcushions Thanks, many handy things on that page!

@ben63 Try setting Device type to just Retropad.
Your current setting only applies to certain games that support analog control. (for example some ps1 games)
I've noticed some issues with my controller when I had the same setting, so I only set Device type to Retropad /w analog for the PS1 and N64 games that support analog control.
If you set device type to Retropad and Analog to digital to Left analog, you can control the game with both dpad and the thumbstick.
Also don't forget to save your settings (either to the game or the core).