The interactive program might have made it too easy for us to follow the wrong track for a while when we were working on the digram-theory. However, once we were on the right track, it made it really simple to try different attempts at character substitutions.
We also learned the important lesson that it is smarter to try the simpler solutions before assuming that something is really difficult.
Knowing this, we also realized that the fastest way into Stage 3 is probably to attack it with pen and paper when doing the first frequency analysis. Since we did all that with programs, we missed the suspicious characters for a long time. If that had been done manually, one would quickly have seen the interesting patterns formed by these characters.
Once again the KISS theory had been proven...