I certainly fall in the Stable Time Loop Camp. I don't think the TT will go beyond the scope of the case files for a few reasons. The first being that traveling through time is difficult and the more time you wish to cover the more energy it would take as per CD. Secondly, I think there is WoJ that Harry will break all the Laws of Magic before the BAT. I assume it will be similar the way he has broken the others, (technically, i.e. Raising Sue, Molly's mind in GS, etc) Thirdly, with Harry fulfilling more Starborn attributes he is becoming more a fulcrum thus making affecting Harry the best way to affect outcomes. Lastly, fixing all the story lines by adding prequels, in essence, feels sloppy and cheap. This series has a structure and I have enjoyed uncovering it.
I would be fine with a Quantum Leap style with either TTHarry being inside Past Harry or maybe helpful janitors in train stations. Esp with Bonnie as his Ziggy being able to remember everything from Harry's memory.