I thought the data you posted is what you were sending to the pedal and the amp?
Anyway, if the amp doesn't have a concept of songs, then your plan would depend on this question: Is the first patch used on each song unique (not used on any other song)?
Since you can't configure the data the pedal sends, you will need to select songs in BandHelper based on the first program change value for each song. If multiple songs use the same patch, BandHelper won't know which song to select.
If this setup doesn't work, then the normal approach would be to get a different pedal that you can program; attach to each song a preset for each patch used in that song; then use the pedal to select from among that song's patches. In this case there's a one-way flow of information from the pedal to BandHelper to the amp, and you could change amp patches either indirectly from the pedal or directly from BandHelper.