Hi! I've taken a while to respond but anyhow, thanks for tagging me, wouldn't have seen it otherwise.
As godreborn has mentioned, as far as I know all Nintendo DS homebrew uses ndstool to build ROMs, and it supports nitrofs. When I was first setting up the UndertaleDS project I used the devkitpro examples (
https://github.com/devkitPro/nds-examples) as a base for my Makefile. You can find an example in the filesystem/nitro_fs folder. The way you do it is just by having a "nitrofs" folder where you put the files. Then, you add it to the ROM by using the -d parameter of ndstool, and you can access them as you would access any other filesystem using C, with fopen, fread, fclose... (preceding the path with "nitro:/<path>", for example "nitro:/backgrounds/image.png").
Be aware that the default implementation for the "filesystem.h" library on devkitpro has an issue where it only works when the nitrofs is smaller than 32MB (that's due to it using GBAROM instead of accessing the cartridge for some reason). I fixed that by changing a couple lines in UndertaleNDS, and I still haven't hit a limit in size (you can find
here my modified nitrofs.c at and the corresponding "filesystem.h"
here).
I haven't taken a look at neither DS Game Maker nor any of the other utilities you've mentioned, so I don't know whether it'd be possible to do the same on them.
Hope this maybe helps?