La Noire and Heavy Rain as "Most frustratingly bad story"?? Ha, perhaps you just don't like these types of games, as their stories are far from the most frustratingly bad. Frustrating, yes, but not bad IMO, and definitely not the worst. Ha.
Have you ever played Dead Island? That game had a frustrating story, whereas it made no sense, and nearly ruined the fun of smashing zombies with electrified katana's.
Overall most frustrating game for me though, was Driver 2. I was stuck on a single chase mission towards the end, and still have yet to finish that game. Lost my memory card a few years back, and hadn't had the will to try to run through that game again.