"Yeah, we figured. When she's got a moment let her know there's a way to undo it, we're working on it, we need her."

        "I will convey that."

And someone gets Loki a room and her own computer. Or a pen, if she'd prefer that.

Computer's better. Allspeak works on typing. She writes up the long version.

And at some point the busy Princess can be apprised of the plan. 

         "What do we know about this Danvers woman?"

"Nothing. I don't love it but we're running with what we've got. If we get a sign that the stones are on our side even without her then we can move faster, but without something really convincing in that direction I think we've got no choice but to stick to the plan."

        "What do we know about the engineering problem?"

"Also nothing. I was expecting that part to make more sense once we've grabbed Fury's stuff and looked into it a little. Natasha's trying to figure out where to look right now. ....I saw the dampeners on the train. What's the top speed vibranium can handle?"

      "Is this related to -"

"This is not related to the engineering problem I needed to be alive for, but since there's going to be a Thanos fight take two I'm thinking how to make it go better than take one."

When she has finished her letter Loki attempts long distance monologuing at the local space stone, introducing herself, describing her history with its alts and the concept of alts, apologizing for the existence of space it cannot reach, demonstrating the teleport, asking if it would like to defect.

She is not surprised that it doesn't appear in her hand.

She is surprised that, with the tiniest crackle suggesting that in some fraction of possible ways it is here while in all others it is not, it addresses her, in the same not a voice as her own:

Do something interesting.

She amends her letter and departs her room to look for someone to report to on this.

Engineers are huddled over a holographic projection arguing excitedly.

"I don't even know what they're working on," says Natasha, "we haven't got Fury's hardware yet. You need anything?"

"I need to be heavily involved on - stylistic approach, and probably more than that," she says. "I didn't get the rock by talking to it from where I was standing, but it did talk to me, which I wasn't expecting, and it wants me to do something interesting. The bad news is the last time a space stone wanted me to do something interesting I spent the next several subjective decades managing a war with an evil god, the good news is it bothered acknowledging me at all."

" - okay. So its sensibilities for interestingness are -"

"...not as bad as they could be? I have seen worse aesthetics. Running entire universes. The first thing I should actually try is see if there are any Ardas adjacent to here, I checked for worlds I've visited before in case the map loops around somewhere I've been to here, and I can't check for alts-wherever-they-may-be with my version of teleportation, but I didn't check for a new Arda and I can because they have lots of the same locations, and the multiverse is infested with them. An Arda's usefulness and potential immediate-term interestingness depend a whole lot on when it is, we find them all over the timeline, they're on rails till someone visits, but I might be able to harvest help of some caliber or other."

 "Yes, that sounds useful. We're in the rounding-up-allies stage, the more allies the better."

"Mmhm -" She checks for Tol Eressëas, space and flat versions. Safely Technically Not Valinor so she won't bother the Valar in her landing (she's not Elspeth and can't just assume she'll be forgiven for showing up on Taniquetil), safely Technically Not Endorë so she won't find that it's been geographically fucked by a war with an evil god and too different to teleport to.

Space Tol Eressëa goes. 

She pops back. "Good news, you have an Arda neighbor! They're a Space Arda, too, they'll have spaceships. Now I have to figure out what year it is and whether anyone I know is alive."

Natasha looks like this happens every day, or at least enough days she's stopped having any expectations about whether it will. "Do you need anything to accomplish that?"

"I do not, but it might take me a while to find out - I should make sure now if it's, uh, cinematically poised to have any main events I could avert happen, but if it's in between things it can wait a few days if that would be more convenient for any reason."

"Thor's helping them teleport around picking up hardware, so I don't think we urgently need you here for anything."

"Okay, cool. I will go try to get you some help." She scoops up her computer, notes that the place has an Arda neighbor but obviously that's not going to help them find her since they've already tried finding Ardas from everywhere they've mapped, and goes back to the Tol Eressëa and turns into a bird and looks for an Elf to ask what year it is.

There are some Elves at the shore of a big, lazy river. They're naked (they are of course not Elf-naked) and eating flower petals.

They'll probably think she's a Maia and even if they don't they're Elves what are they gonna do, stab her? She lands on a treetrunk nearby and says by illusion, "Excuse me, what year is it?"

The Elves look at each other uncertainly, then at her. “1530,” one of them offers after a moment, as if they don’t think about this very often and expect Valar to even less often.”

"Thank you." She flies away a bit and starts trying candidate places on Endorë. It'll be different from the other Space Arda, this is much later - she's not sure how a lot of it would play out in space, but some of the landscape may still be there. She doesn't manage and winds up aiming for well above an Endorë ocean so she can aim visually for land. She does this invisibly; no point alarming Melkor.

From here she can see that Endorë's continents are not green and its water is not blue and there are giant, low-hanging clouds of ash. That's probably why the teleport failed.

Yikes.

She pops around and around, assessing, looking for signs of civilization.

There are fortresses. There are some airfields. 

Any of the fortresses helpfully eight-pointed?

These fortresses make even fewer concessions to Elven sensibilities than the one of Maitimo's she looked at. But some of the airfields do have a familiar eight-pointed star.