New intermediate goal: creating a demo that runs on a standard Amiga 500.
This means kickstart 1.3 is back in the picture.

First step: let there be music!
Most of the mod-player libraries I tried won't work on KS1.3, but then I found the awesome (and very recent) PTPlayer, made by PHX in Assembler.
It's not entirely system friendly, but for a demo, that'll do.

That was - again - a steep hill to climb: figuring out how the compile the library and use it from a C program.
The compiler started throwing weird stuff around like FAR and NEAR data descrepencies and what not. Errr... Whut ?

But after my usual approach: keep banging on things untill it works - I ended up with something that worked and that didn't look all that bad.

Code here on Github.
It's a small wrapper function that enables me to just write 
play_mod("somefile.mod")
and be done with it.
Nice.

Lessons learned:

• how to compile assembler code to an object
• how to link that object and call it from C code
• how to load a file from unknown size into chip memory
• how to clean up after myself, so I don't have to reboot the Amiga after each test because of a crash 

Update:
If you want to target 1.3 and want to be system-friendly: Stingray has patched the PTReplay.library to work with 1.3. Awesome!