All she needs is to step within 300 meters once, and need to cross more than that minute distance for it to work. Including when she's unable to keep going on account of exhaustion.
For the millionth time, danger sense will alert asuna before she gets blitzed by its light-speed attack speed. She can basically read all of warrane's attacks like a book, and so, she has plenty of warning time to move out of the way, and even knows what actions to take to dodge it. Even without any speed amps, and even if she only heeds the warning with 0.1 seconds left to dodge, she’d still be able to move 343 metres assuming it’s bare minimum hypersonic+. Way more than enough. And like I’ve said before, she’ll immediately adapt and change strategies once she see’s this, especially with Genius Battle IQ and reactive evolution. And It's very unlikely, if not outright impossible for asuna to get exhausted before warrane for reasons below this.
That's more a matter of the human mind being wired around a reset on their 24 hour sleep schedule. Removing that just causes everything to start bleeding together, making each day indistinguishable from the last, it's not something that strictly degrades function, and definitely not to a degree comparable to Asuna having to also deal with the exhaustion and her nervous system wearing down from the lack of rest.
The main reason they don't have infinite stamina is that
they are noted to get strained from continuous energy use, but all they really need to do in order to recover from that is just use Energy less over a prolonged period (not even be inactive persey, given Silas "resting" by being at an amusement park for 14 hours straight, and Xander and Warrane collaborating to make the mother of all mancaves in what might have still involved a little bit of Energy use, given the former's specialized in Trigger tech). Triggers lacking Supernatural Willpower in this comparison really is more like, an effects vs mechanics argument, both of them are ultimately accomplishing the same thing, Triggers just don't achieve it through their willpower having Supernatural capabilities as opposed to their physiological quirks.
Asuna basically had her nervous system destroyed as a result of taking a hit for shizu as well, (kedron fight) since it's spread through a humans entire body. (Including spine and nerves which definitely also got destroyed) So Asuna didn't just survive getting her organs obliterated logically too. And even when that happened, she kept fighting like nothing happened at all. Im pretty sure getting your nervous system destroyed, or at the very least sent into a freakin frenzy, and acting like nothing happened is way more damaging than having it get worn out. So logically, Asuna is definitely not going to be outlasted that way.
If they use energy less, then that will just leave warrane more vulnerable. That means he can't use energy shields or weave and dodge as much, either. Asuna has never been shown to get strained from continuous magic use, for example, either, and neither has anyone else in the novels, since it's basically imagination manifestation, not much stamina needed. So warrane is basically relying on limited time, whilst asuna isnt. That combined with her shown endurance above means that asuna will definitely be able to fight for as long she needs to, especially since you've said yourself he will get strained and fight less effectively as a result, whereas asuna most likely won't. She's not gonna let him rest to get that energy back, either.
And on the topic of warrane trying to hide, wouldn’t it be pretty out of character for him to do that? You’ve said yourself that he’s one to go for the kill, and his profile literally says: “Warrane is obsessive over his level of power, wishing to exercise and enhance his use of energy as much as he possibly can, stepping over his allies if needed. He also bears a degree of arrogance that causes him to flaunt his capabilities and go into risky situations he could otherwise avoid.” I seriously doubt he’d want to do that now that it’s come to my mind, which gives Asuna, once again, even more opportunities to win via one of her wincons, or if not, allow her to adapt to him way more easily since he’s going all out, which is gonna drain him of his energy and require rest like you’ve said, which Asuna isn’t going to give to him as I’ve said above
Dodging attacks and returning fire isn't the same thing as having to move in two directions nearly simultaneously in order to reliably keep a bead and not stay in his range. Crunch's the speed of light and Random Events just happen on top of her, both are liable to have the potential to work.
...She could move Backwards. Her attacking and dodging at the same time isnt required, either, she can play defensively at times if for some reason she is forced to get relatively close, and even then, with turbocharge alone she is twice as fast as his reaction speed (or ten times if he doesnt use flashstep) and thats not including supercharge, which is a 100x boost. He wouldn't even get a chance to use crunches if that happens. Crunch may be lightspeed, but all of his other speeds, including reaction and perception, sure isn't. So he won't even be able to push the button in time to hit asuna even if we took away that danger sense of hers. It might make Asuna lose her bead on him, sure, but she’ll definitely be able to just locate him and continue the fight.
He can travel at 6 Kilometers per second via just basic movement alone, he'd be back in a little over half an hour even without Flashstep.
He is, Valhalla takes place on an altered Earth
Keyword: Altered. I don't know exact details obviously, but hows he going to direct himself back to NYC without a compass or prior knowledge? If by altered, you mean like different countries and cities and stuff, then i don't see how he's getting to NYC from Japan, which is a place he might have not been to before. You can't just figure out where you want to go if you dont have any sense of direction either. Still, if he can come back even then, asuna simply sending him to space or maybe even the moon still isnt out of the question considering the nature of magic in bakuhatsu, (About envisioning space, asuna could simply envision viewing earth from space like on the ISS, and send him there) and the fact that asuna is definitely willing to kill or go to extreme measures if necesarry, especially if the person is a killer like warrane. the only reason she hasn't gone to space or tried to send chidori there is, 1, She doesn't currently need to go to space (She will later on tho, thats the plan at least), and 2: If she did that to chidori, then she wouldn't get kiannas sword back, which was why she fought her in the first place. (She wouldn't have known chidori would have came back though, but you get the point. If she has no reason to NOT send warrane to space, then she'll do it when she see's she can't beat him by killing him with Explosion or Thunder magic and the like, at least until she makes a skill that can bypass that, but she'll probably try this first)
It would also mean warrane would have no hope of coming back regardless of how deep into space he is, since he hasn't been shown to survive a vacuum (To my knowledge) and he doesnt have things like "Spaceflight" or "Resistance to cosmic radiation" listed either. So if that happens, he's screwed even if he doesn't die from it, so basically, he’d have no hope of returning once that happens.
He definitely has means of breaking her focus by just getting aggressive and trying to hit her with a Random Event or Crunch, so that's another way he could neutralize it.
Asuna hasn't broken her focus before, even against enemies where she had little time to think or otherwise do so. Plus, she'd be expecting it anyway, especially once she learns his moveset and his range. Even if she did have her focus broken somehow, Chidori has stated that if at least 2 of 3 magic factors are not disturbed (those being willpower, mind, and condition), one can still use magic effectively (Vol 1 Chapter 5) which was also shown in the kedron fight (Asuna still being able to fight and use magic despite grevious injuries) so asuna's willpower alone will ensure magic will still work, and that goes for the clones too. And even if warrane disrupts that by somehow injuring asuna to the point where she could die alongside disrupting her focus (Nigh-Impossible since warrane is very unlikely to even land a hit on her for many reasons above, and also that Asuna would be extremely difficult to fatally wound in the first place) Asuna can use playback or riftways to temporarily escape and quickly heal herself and drop back in a couple seconds later, good as new.