Update: I solved the problem on my end.
All I did was swap the failing SD card (SanDisk Ultra 16 GB, A1 class, SDHC) to a different one (SanDisk Extreme 32 GB, UHS-1, SDHC) and the new kernel(s) boot without any problem. So it seems that with the kernel upgrade, the support for the former SD-card broke, but it still works for other types.
If someone wants to debug this, I can do checks because I have setup serial console that I can plug in whenever necessary. For now I will not do any further research on this, unless someone asks.
