I can create a customized live Alpine Linux ISO, using mkimage as described
in the wiki
<https://wiki.alpinelinux.org/wiki/How_to_make_a_custom_ISO_image_with_mkimage>
just fine and it works perfectly. I can even go one step further and modify
and build some packages to a local repository and then tell mkimage to use
them, and it also works perfectly. As long as I don't modify the
"linux-lts" (i.e. the kernel) package.

My final goal was to create and use a custom kernel,  one built with only
the modules I need. I did that, but when I tried to create a live ISO with
it, the process fails right after signing the "modloop", and the error
message is:
"cp: can't stat '/tmp/update-kernel######/boot/config': No such file or
directory"

I tried to simplify things and instead of using a custom kernel config I
just used the default ones. The only thing I changed was to update the
kernel makefile and set march and mtune to native. After that I simply
executed

abuild checksum
abuild -rd

Then I passed the path of the local repository where the package was
created to mkimage.

Any idea of what I might be doing wrong? I don't know if that might be a
problem, but I am doing all that while running Alpine Live (that is, Alpine
was not installed on the machine)