I have improved my previous design even further. Because I realized that I did not need to calculate both the normal and the inverted carry out to have a fast ripple carry. One of the two suffice, however they do need to alternate.
The logic I used to build this circuit is:

This removed a lot of the logic, therefore it could be made smaller (and faster, since I did not needed to place that many repeaters). This design is 12 blocks long, 10 block high and 4 block wide (for 2 bits).

However when I started testing this adder I got very strange (inconsistent) results, which is possibly affected by its orientation and its position relative to chunk borders. Since some carry seem to be faster then 1 tick, or even instant. The results for the adder in the world download are 16 ticks for 16 bits and 11 ticks for 8 bits. But I also got 15 and 17 ticks for 16 bits in other situations. Not entirely sure what is causing this.

So if you have a better explanation why this circuit gives different results depending on its orientation and location, please leave a comment.