Hiya!
I didn't read the whole thread, so I'll just say my peace and how I handled Time Travel in a SUPERS! game I run every now and then.
Time Travel involves two possible outcomes of any particular event that the PC's become involved in. They are "Eventualities" and "Impossibilities". It takes some copious amount of note taking when the PC's are "in a different time", but it's worth it.
Basically, if the PC's go back in time to, say, stop a car from crashing into a building for some reason...and they Succeed: Then that even was an "Eventuality". If it was allowed to happen, then EVENTUALLY the time would turn out what the PC's experienced in their 'original timeline'. But...if they Fail...then it is an "Impossibility". This means that no matter WHAT the PC's do after failing to stop it, including trying to go back in time to try again...they WILL FAIL. There is absolutely NOTHING that can stop it (and I'm the GM, so I just make sure it happens).
For example, the PC tries to use a "Storm Powers" to use a strong gust of wind to slow the car to a near stop as it gently bumps into the front door of the building. Yay! The PC's succeeded! That event was at the "Eventuality" stage in the timeline (if the PC's weren't there, it would happen). Crisis averted and when they go back to their own time, all is good...or at least not the way it was. BUT... Lets say the PC uses his Storm Power to use a strong gust of wind to slow the car to a near stop...but rolls badly and fails. Well, that is now an "Impossibility". No matter WHAT they do, when they get back to their 'timeline', whatever event occurred due to the crash into the building DID occur. The PC's can go back over and over, and SOMETHING would always cause the building to 'collapse'. The car hits a power pole which falls onto the building lighting it on fire...or the car causes a bus to swerve and run into the building, or the car they thought was the one wasn't, and 30 seconds later the real car runs into it, etc, etc.
Anyway, that's how I managed to overcome the "problem" of Paradoxes and such. There are no such thing. If something would cause a Paradox...then it is already an Impossibility. You can't go back in time to prevent the experiment that gave you your time traveling powers, for example.
Maybe that will help with the OP, maybe not. Hope it does.
^_^
Paul L. Ming