Time would probably heal itself from changes in the past:
Young physicist 'squares the numbers' on time travel
Simulating quantum 'time travel' disproves butterfly effect in quantum realm
So, you could probably try anything in the past and the changes would only be small or nonexistent for the present.
But no one really understands time anyway. Check out "Julian Barbour - The Janus Point - A New Theory of Time". It's very interesting.