The built kernel boots with a black screen and no further sign of acitivity. Fastboot flashes without errors but flash offsets are probably wrong. Only known working kernels have a different ELF file format.
There is one tool avaiable for unpacking Sony's ELF boot format into the normal ANDROID format: libbootimg
Sadly, even unpacking and repacking a working prebuilt kernel doesn't seem to work.
I had more luck with mkelf.py script from Sony. You can loosely follow the tutorial here. This time unpacking a working kernel elf image and repacking it with mkefl.py worked. Needed to change only a few bits with vbindiff. Now we only need to find a working set of offsets and image parts to do the same with a custom kernel!
Here are some links describing the problem with Sony's boot format: https://github.com/chenxiaolong/DualBootPatcher/issues/181 https://github.com/Tasssadar/libbootimg/pull/2/commits/8986984b5d618be0b753e55d6b9d9d1744bc4094 * https://books.google.de/books?id=2qo6AwAAQBAJ&pg=PA313&lpg=PA313&dq=sony+boot.img+format&source=bl&ots=0mtMMle9eZ&sig=adCVtfarXK9cticvd5qqYA6g39Y&hl=de&sa=X&ved=0ahUKEwjgp5mfx5XVAhUHWRQKHWSeDZcQ6AEIQzAB#v=onepage&q&f=false