I'd argue there's no need to assume that either ST:TFF or TAS "Magics of Megas-Tu" actually took our heroes all the way to the center of the galaxy. I mean, that's not even a place a starship could visit in theory! In the former movie, a madman ordered the ship to fly in the direction of the center, but Kirk said this wouldn't work because of an obstacle; the obstacle could have been quite proximal to Earth. In the latter episode, our heroes were to observe the core, and this could and probably should take place at a distance - the larger, the better, really. Neither outing includes dialogue indicating they would be
at the core, or anywhere near it.
As for nuTrek speeds, we have moved from "speed of plot" to "speed of cut". In both the movies so far, travel has involved both events and lack thereof, and the latter have been mercilessly cut - so mercilessly that we can't really tell how much was cut.
Earth to Vulcan - minutes or hours? Both are possible, the latter is more likely, considering the amount of stuff in need of cutting, such as Kirk, well,
sleeping. It could really be days, even.
Earth to the edge of Klingon space and back? In one direction, long enough for Kirk to come back to his senses (so probably weeks...). Yet in the other, short enough that Carol Marcus barely has time to reach the bridge (hopefully remembering to use those lightning-fast turbolifts rather than running the whole way). Of course, Kirk would be highly motivated to move much faster on the return trip.
And therein lies the catch: high warp is
really different from medium or low warp. Take a realistic ocean adventure: a ship in a hurry might be 20-50% faster than a ship not in a hurry, and would need to take suicidal risks to reach such speeds. Then take Trek and its supposedly exponential warp scales: a ship in a hurry might well be 10,000% faster than a ship cruising idly...
That's what we always have to mind when studying Trek speeds: fast is not just faster than slow, but astronomically faster. And, just as with a steamship trying to boost speed by 20% with the engineer sitting on the safety valve, it comes with immense risks. In TOS already, it was made clear that warp six was fine, warp seven was the textbook way to hurry, and warp eight required you to have your last will and testament properly signed - yet the starship could easily do warp fifteen. Our heroes took the risks, and won their gambles. Many a skipper not being filmed for posterity probably perished trying to exceed warp eight with that warp 15 -capable hardware, though.
The massive problem with that is that our heroes never mentioned such things, nor acted as if those would make any difference. It would be much like Stargate SG-1 having all the adventures they did, but never bothering to show or even casually mention the actual stargates!
Timo Saloniemi