After some time in vacation and between the year I successfully managed to patch the game in order to replace the first dialog of the first scene.
I wrote how I did it as usual in my
blog post (corresponding code is also uploaded in
github).

However, to make it clear: I don't know if this method works every time. It is still not 100% solved but a way to go. I think the textblock patching works quite fine but the dialog pointer changing is very tricky and not 100% fail-safe yet.
Because this is new to me: Does it makes sense now to create an official entry in the
https://www.romhacking.net/translations/ section to upload resources and have a working context with other interested users?
Maybe translators would like to download the
925 CSV files I extracted to start translating as Chicken Knife suggested. Every UTF-8 file corresponds to a textblock that can be patched in the HBD1PS1D.Q41 file. The name of the file (do not change it) is the ID of the textblock.
For testing, I entered something for the first dialog and patched the game to make the screenshot you see above.

A big help during research was a user named rveach who investigated translating DQ7 years ago.
What is still missing is patching in-game text, status messages and dialog options.
Because of my full-time job I am not sure how much time I can invest, but for questions I will be available.