The PCB layout is finally done. There are a few things that can be improved, but I'll probably leave them for later. It's very likely that some minor fixes will be required, so the improvements can be done at the same time as those fixes. One thing I had completely forgotten was the fact, that the reverse voltage protection is not needed - it's already integrated in the charger IC.
Since I read the email that [OSH Park] started following me while I was mostly done, I decided to make the PCB purple. I also added the jolly wrencher.
All current files are on Github.