Ok so double posting to bump this topic and to clarify things:
[03:55:30] flying fox: ok last time for confirmation and I'm dropping it: TA mode for times, TA mode not needed for rings and scores and we can time travel?
[03:55:48] Thorn: that is what the rules state, so that is what I will say
* With the exception of items designed to change the timer, using any method to reset the timer to zero in the middle of a level is not allowed.
We are allowed to time travel as the timer only resets to 5 minutes not 0, so we're not breaking the general rule.
EDIT: Trust me to use post #666 to quote what Thorn said.