I would love to see a time travel story with a twist and a dramatic human element. Actually, a good example of this in recent times is the novel The Time Traveler's Wife by Audrey Niffeneger. The twist here is the protag has a genetic disorder that makes him time travel, and he cannot control it. Take note: the time travel does NOT work in the standard way. The dramatic element is the story is actually a LOVE story between the time traveler and his wife. Take note: the novel is NOT primarily about time travel; it is about the love story. Of course, the time travel is an integral part of the story, which is why I enjoyed it. :)
What dramatic human element/situation can you fix/solve using non-standard time travel as a MEANS (not an end)?