Okay I just misunderstood what you meant by quit-out. Xbox One is ~10seconds to for the whole process. I'll have to do a playthrough and find which which ones are skippable.
I'll copy over what I put on SDA.
I currently have a time of 3:29:52 pending on speedrun.com. It was far from a perfect run, specifically the Ice Temple was pretty terrible. I didn't use any cutscene skips since I didn't know how that works in a single segment run.
[quote]
The estimated time it takes to quit out and load back in is a little under 13secs on the Xbox 360 with a disc and installed to the hard drive. I don't know about the time taken on the Rare Replay version for the Xbox One, but I imagine it's faster. [/quote]
It is slower by a large margin (~50sec per quit). Most of this time is the Xbox One loading up the 360 software.
By what I can tell most of the timesaves in this game are going to come from optimizing combat.