With some creative routing, I've increased a day trip in economy from Frankfurt to Munich to collect something for work (1000 + 250) to a much more respectable (3500 + 873) for about 60 EUR extra. However it does mean that I have to leave Budapest on the same aircraft I arrive on 40 minutes earlier. I'll have checked in for all segments from Frankfurt, can anyone see any problems getting back to the gate on time for the outbound? Also are LH responsible for getting me back if I miss this or is it deemed to be the start of my return trip and therefore my fault?

...if it all goes wrong there's a night train back via munich for 140 EUR