I give you the professional word of a long time fan of the Sonic The Hedgehog series, that time-travel... would be an awful thing to do.
This may be an unrelated comparison, but from my experience with video games and time travel plots, it does nothing but mess up the whole continuity, time flow, creates more plot holes, and in general is just uncreative. In most series, doing 1 time travel is very difficult, because that alone creates plot holes found by fans and causes demand to go back again and fix something, and then later on they end up resorting to time control for various things, and it all just gets confusing and annoying.
If you ask me, time travel is a big no-no.