After reviewing your write-ups, I tested and compared your code on the following
A simple repetition 5 code. It is the best you can do in a maximum entropy situtation (assume uniform random distribution of 0's and 1's in data) in terms of number of bits correct.
Team Bravo used a repitition 6 code, but instead of guessing randomly in the case of 3 errors/6 bits, they guess intelligently, using the idea that for an image, neighboring pixels tend to have similar colors. This works considerably better than a straight repetition 5 or 6 code, as you can see by comparing with the previous image.
Team Omega tried to program a repetition 5 code in a clever way, and to their credit it was quick, however it was not correct and they do not have as many errors as they should. (If programmed correctly, it should give something like Team Alpha's code.)
My code was a [13,11,9,7,5,3,0,0] "weighted repetition" code: For each byte, I repeat the highest order bit 13 times (or rather 12), the next highest order bit 11 times, and so on, and just ignored the two smallest order bits. This capitalizes on the fact that we are working with images, and the highest order bits are most important. One can potentially do even better by combining this with ideas from image processing, as in Team Bravo's code.