Okaay, so here's my final review of this process.
For me, cooking the ink for longer and letting the husks soak overnight didn't make any difference to just letting it cook for a hour. The ink is thicker, yes, but funnily enough it's not darker. It's also not substantially different to write with.
Compared to the walnut ink from kalligraphie.ch I bought, mine is lighter in colour. The main difference is that it is oilier, kind of like iron gall ink. It also covers the nib similar to IG. This leads to wonderful hairlines (thinner than with the ink I bought).
To sum up the good and bad things:
++ Cheap!!
+ Easy
+ Collecting the husks was a fun activity for the kids
++ Hairlines!!
- Not as rich in colour as expected
Finally, a picture of the short cooking time batch, the long cooking time -> overnight soaking -> long cooking batch and the one I purchased: