@zukov At the moment there is not much, the developer seems to works on and I only help with tests. I also bring him your finds, and there is a thread where we discuss things: https://github.com/dreamer/dosbox-staging/issues/144
In brief, he thinks that it's in the src/hardware/vga_draw.cpp, around C_UNALIGNED_MEMORY lines.
And today I also find that PCNBench tool has the ability to choose in what screen mode to run it, so:
8 bpp: no bugs http://kas1e.mikendezign.com/aos4/dosbox/badcolors/pcnbench_8bpp.jpg
15 bpp: have bugs http://kas1e.mikendezign.com/aos4/dosbox/badcolors/pcnbench_15bpp.jpg
16 bpp: have bugs http://kas1e.mikendezign.com/aos4/dosbox/badcolors/pcnbench_16bpp.jpg
32 bpp: have bugs (much less distortion, just green color swapped) http://kas1e.mikendezign.com/aos4/dosbox/badcolors/pcnbench_32bpp.jpg
From screenshots above, probably it means that both 15 and 16bit modes suffer from PC vs no PC modes (that why it works on other platforms) , while 32-bit mode seems to suffer from some easy wrong byte orders, and strange if that will not happen on other big-endian platforms. As on amigaos4/morphos we use PC modes only for 15/16 bits (right?)