I made a breakthrough yesterday night and could fill most of the gaps.
There is still a lot to do. Part of it is simple and just requires trying various combinations until the correct one is found; I should be able to do it the next night I dedicate to the encryption. The rest is less simple and requires finding the remaining (and therefore less obvious) correlations between bits. However, the closer I get to the goal, the easier it is to see if a certain formula is correct or not.
Sprites are finally good enough to show a screen shot.