Problem with LUKS Password Entry with non US keyboard and special characters

When I boot the live CD (USB, actually …) I do select the correct keymap, as that is in the boot menu.
… I’ll type the wrong characters otherwise …

Your issue could be fixed by including your (correct, custom) keymap in the initrd.
To achieve that, the “keymap”
and possibly the “consolefonts” keywords
should be in the HOOKS definition of:
/etc/mkinitcpio.conf

mkinitcpio - ArchWiki

Yes, this could be improved - as of right now, the user set keymap isn’t included
which causes problems with password entry
for anything other than an english keyboard.

My workaround is:
choose a simple password when installing, so I can successfully type it on a non english keyboard -
and amend it later.