There might be shortcuts, but since their current greatest ability to address problems - especially Enemy-scale problems - in other worlds is the Tesseract, it seems efficient to go places that are adjacent to Edda and therefore within its jurisdiction. It is still grouchy and won't help with anything Loki can't do her own fact-finding work on, so it's worldleapers. Cam goes alone first - it's unlikely that he will land in a star, but not genuinely impossible, and he can then find somewhere comfortable to land and go fetch Loki and whoever else is coming along.
For a while, the worlds they find are more or less equivalent to finding new civilizations within Edda. They have to be discovered differently but they're just places, with people, no alts, no Ardas. They are investigated and put on file for their resources or needs; if there's anything really pressing (planet about to collide with its moon, that sort of thing) Loki fixes it before moving on. Maybe eventually someone from one of these worlds will turn out to be really interesting and they'll be delighted to discover alts of them too but they'll have to distinguish themselves some way in some world first.
Then there's another Arda.
"Another one?" Loki asks.
"Complete with mutually intelligible Quenya," Cam says.
"Enemy an ongoing problem?"
"Yeah, this time I will have a conversation before I destroy him, wouldn't want another close call. Let's go meet the local Noldor."
Where are you, local Noldor? Loki and Cam are there now too.
He blinks at them.
He's sitting on his throne looking relaxed and perhaps bored and in reality conducting thirty conversations at once. He concludes them while slowly blinking at the new arrivals.
"...hello," he says. "Teleportation or really excellent invisibility?" And he waves the guards back.
"A war, I hope! Do you happen to also have magic up your sleeves that would let me efficiently convince you my side ought to be the winning one?"
"I don't know what information you'd require; if you've met nine of me you probably have more information about whether there's a deadman switch setup than I do. I also cannot help you, we're currently sworn to a ceasefire, though you said that like you don't expect to need much help."
"The war escalated to the exchange of extremely destructive weapons and we had something cobbled together from the Silmarils that would have killed him but would have taken half the planet's population with, and so we negotiated. He's not allowed to hurt anyone."
He elides Elspeth, because this woman looks like Elspeth's mother and Elspeth's mother was purportedly likely to want him dead. Though if this woman got along with nine other Maitimos then probably she doesn't have the same reservations - or the other Maitimos had more discretion -
"Anyone I call a citizen, a privilege I've been abusing."
"Did some of my counterparts know? What information should I be asking around for? Not that I expect the Valar'll kill you on sight but I also don't expect very strongly that they won't do that."
"And the ceasefire's weird? The Silmarils being weaponizable to destroy the Enemy: is that weird?"
"They can effectively stop time within a radius, that works fine on Valar. They can tweak what they do to the stuff in that timestopped radius, and one thing is 'have every atom decay at a different rate' and we didn't get a chance to try it but given how quickly he agreed to generous ceasefire terms I'm pretty sure it would have worked."
"Getting it to work as offense took us years! Though my father's dead and could probably have done it in a couple of months. I suppose it all depends on when you got your Silmarils back relative to when your hand was forced."
"He was assassinated by his half-brother when the Noldor had a civil war, three hundred fifty-some years ago."
"I should congratulate my counterparts on defusing it better. I managed, but it took too long and cost too much."
"Melkor pardoned in 1400? My father makes the Silmarils in 1450 and then starts working on various other necessities for an independent Noldorin kingdom? Gets provoked into pulling a sword on Nolofinwe in 1490, gets exiled by decree of the Valar, Melkor extinguishes the Trees and assassinates Finwe in 1495?"