And the lemmings part?
The "indirect control" part is the Lemmings part - you don't control Lemmings directly, but you do so by putting stuff in their way.
This is super obscure, but as a teenager I once read in some magazine about a game, "
Pac Man 2: The New Adventures", where you controlled Pac-Man indirectly and solved problems "with" him. It always sounded like an interesting experimental kind of game (from an era where experimental games actually got made with major licenses and put on shelves, can you imagine that today?)... anyway I never played it but you might consider trying to dig up a ROM for it, it's always good to look at similar games to give you ideas.
Oh, you should also look at "Lucidity", a recent platformer where you place the platforms in front of the character for them to find their way around. "Eets" may also be relevant.
You know, I haven't played Heavy Rain (though I should), but I have played something similar: a "Choose Your Own Adventure" book. I don't have a high opinion of them as game designs, although at the same time, I think that games are about interesting decision, and decisions that I heard about in HR such as "would you cut your pinky off to save your child?" are certainly interesting.
But my real problem with choose-your-own-adventure gameplay is that it ultimately still feels like I'm experiencing a story someone else wrote, rather than making a story for myself through my own experience. Unless there are hundreds or thousands of permutations (and the work behind writing all those, even for a text-based game, is impractical), it will never give me a feeling that I'm really choosing my own path through events.
Then again, Fallout was a game that had a lot of mini-stories within the game, and I definitely felt like I was occupying my character and directing my own path there. Maybe there just have to be enough choices for me to feel that I can express my own personality (or the personality of the character I'm role-playing).
All in all I'm more interested in games that are "systems" than ones that are based around branches of discrete choices, no matter how dense those branches may be. But it's always worth experimenting, I'd love to see an indie do something new with the Heavy Rain formula.
The time-travelling seems like a logical addition to me - but it does give you the equivalent of being able to basically flip through each and every page of the "Choose Your Own Adventure book"... an easy way to go back and see every different possible path you can go down. To some this might rob the magic and further destroy the feeling that "the story is my own"; to others it simplifies what they're going to do anyway, which is play the game over and over again and see all the content.
I would probably make a prototype without time-manipulation if I were you, and consider adding it later after you see how the game plays. In fact if you prototype this, I would focus on the "indirect control" mechanics first, those are experimental and mostly-unprecedented enough that you'd want to play around with them to be sure you had that core being something pretty fun.
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