The Mononoke has, just from looking, already derived the natures of these ship's radio transceivers and antennas, and provides the specs so the crew can decide what format to transmit in.

The captain looks to Verity. "You're up, just say when you're ready, and we'll hail them."

Madoka (and Homura) arrive on the bridge as well, stepping up onto a platform against the wall behind the captain's mechanical 'throne'.

Her sharp little suit is gone, replaced with a white on white on shimmery aurora-black Barrier Jacket in the form of an elegant dress-coat with a massive billowing train, or possibly waist-cape, rippling with an inner pink radiance.

("You've got this?" Homura inquires quietly.)

"I think so, yes," Madoka replies warmly, studying the view over the back of the captain's throne.

"Will I be the one speaking?"

"You can keep it short, and probably should. Tell them you've returned with friendly aliens and not to panic when we give them a lift? The Mononoke will be going ahead to the planet to serve as a targeting beacon for the Dimensional Transfer, once they're warned."

She nods, and tries to stand up a bit straighter.  "Yeah, I'm ready."

The captain hits a figurative button, and tells Verity to go ahead.

And the fleet gets a very unexpected transmission.

"This is Verity-and-Araeneve, on an alien ship called the DNEV Mononoke.  They have a form of FTL that they intend to use to move the fleet to its destination."  

The person on duty in the transmission room frantically looks for information on their phone.  Legendary Verity-and-Araeneve had been reported missing not long ago, prompting a fleet-wide search.  

"That's, ah, good?" she says, surprised.  "Welcome back.  I'll tell the... the captains.  How soon do they intend to do it?"  She sounds young, and not sure what to do in this situation.  While her job description technically involves picking up any transmission for ships, this has up until now been scheduled check-ins and routine maintenance missions.  

"I'm not staying," she says.  

Turning to the captain of the Mononoke,  "Anything else they should know?"

"Oh, probably," she says, wry. "But that is satisfactory."

The captain twist around toward Madoka and Homura. "Alright, Kaname. You're up."

Yeah, when Madoka said they'd come equipped to transport the entire fleet? She was kinda... talking about herself.

Madoka and Homura share a kiss.

And then a blazing pink Circle unfurls under Madoka's feet. A moment later, she's gone from the bridge.

She appears outside, in front of the ship, gives a little wave, then shoots off towards the fleet in a streak of pink, flying unaided through open space.

The view out front tears apart into dull eldritch colors, swings around, and shifts again.

Minutes later, almost simultaneous with when Madoka reaches the mid-point of the fleet, the Mononoke pops back up into real-space in a high orbit around a planet Verity and Araeneve should recognize.

A pink star appears, a pink sun.

And a fractal, slowly shifting, gargantuan Circle.

And then, all at once, a previously empty section of space is occupied by a fleet, the shining form of Madoka visible to the naked eye in their midst.

That hadn't been much time, though they managed to get a quick announcement out.  There are some local sci-fi conventions regarding the interaction between teleportation and hypothetical FTL.  Without any information on the subject, they decide to play it safe and the announcement includes a warning to avoid teleporting until further notice.  

A fairly small percentage of the fleet inhabitants are in a place where they can view the planet that they just appeared near.  Those get much more crowded as people gather near the ones closest to them as people call their friends over to try and get a look.

Madoka parks herself in front of the biggest, most official-looking window, and waves.

That would be at the front of Citadel of Spring.  A segment at the front of the ship sticks out about a hundred meters from the rest, and it's exposed sides and ceiling are covered in windows.  The room isn't a bridge (the ship control rooms are well-defended near the ship's center, seeing outwards only with cameras and sensors) but it does function as the place where most fleet-wide speeches are given from as well as the location where the legendaries lead the fleet in major religious ceremonies. 

Easily visible within the space is an elaborate abstract mosaic taking up most of the floor space, 150 meters wide and thrice that deep into the ship.  The ceiling rises 70 meters to meet the roofs of the greenhouses which line the interior of the cylinder.  The interior walls before the windows begin are covered in gilded bas relief murals and multiple levels of balconies.  A section at the very front is raised as a stage, and permanent cameras and spotlights point towards it.  

The room isn't especially full, though there are some people filing in to look out of the windows.  One woman in her 60's stands on the stage beside a very large daemon, dressed in a blue and white gown.  A few others in similarly elaborate clothing are making their way to the front.  The woman waves towards her.  

Madoka isn't in a hurry. They've just arrived at their long-sought destination, and probably have a lot to do to spool up for their eventual landing. But she is inclined to wait there and not keep them waiting once they're ready for formal contact.

Meanwhile, back on the dimensional cruiser, Homura ask if she or Eelesia will be teleporting Verity and Araeneve, that is, if Verity and Araeneve still intend to act as intermediaries?

Preparations will take a long time - far longer than it would be polite to make someone wait outside of the ship.  Given that the Legendaries are not necessary for scouting operations and also already involved (through Verity-and-Araeneve), they seem like the obvious ones to start.  

Angie-and-Damantira watch her for a moment while the others inside reach the stage.  No obvious daemon, and seemingly unaffected by being in open space.  They aren't sure what security measures they should take in a situation like this (or, for that matter, what security measures could do anything at all, given that the aliens clearly have either far more powerful Moves or technology).  Furthermore, they have already helped them and it would be rude to assume hostility in such a case.  

Once everyone is together, they try to contact the same frequency that they had been contacted with and extend an invitation to come aboard.

"I'm still here to do whatever I can that's useful," she says.  Verity doesn't express an opinion on who does the teleport.  Araeneve steps slightly towards Eelesia, being more familiar with getting teleported by her.  

A pink Circle unfurls under Madoka's feet, a fractal pattern of rotating pink luminescence. Then an identical Circle blazes into existence inside, accompanied by a dark purple Circle and a light violet Circle.

Madoka teleports from from outside to inside, and a moment later figures appear in the other two Circles as well. Eelesia, with Verity and Araeneve, and Homura, who strides over to stand at Madoka's shoulder.

"Thank you for having us aboard!" Madoka says serenely. "I'm sure you have questions."

She quietly re-casts Heaven's Gaze and pilots the little orb of pink light to hover at her other shoulder.

"Quite a few, yes.  Though before then: Welcome to the Citadel of Spring.  We are Angie-and-Damantira, one of the Legendaries of the fleet."  She also introduces the others who had come over to join the greeting party.  One is a fellow legendary with a small Azelf daemon, and the other two are elected council members who handle certain ship-wide policies for Citadel of Spring.  

They seem irritated and concerned over Verity-and-Araeneve.  That Verity is currently dressed inappropriately by their standards by not wearing blue.  More importantly, what Verity might have said to the aliens, as a well-known discontent.  None are remarking on it openly, though a few of the daemons glare at Araeneve from where they've moved away from their humans slightly to have their own conference.  

Madoka introduces her greeting party with the odd mix of formality and casualness typical of Childan culture, and politely ignores the irritation and concern.

"I'll be glad to answer any questions you have. That's why I'm here, after all! Though I should firstly clarify that we were quite happy to shorten your journey without recompense. It was truly the least we could do after learning of your circumstances from Verity and Araeneve. I should secondly clarify a matter of trivia before there are any misunderstandings: across the wider breadths of existence your people's duality of body and daemon is actually quite unique. I, and indeed most individuals across the panhumanity of the totality of existence, are singular beings," she switches to speaking through her spell, "though I am easily capable of holding two conversations at once."

Araeneve had already begun informing the daemons of the ball of light they could speak to, figuring it might be relevant soon.  The others determine quickly that they will form two groups - Damantira and one of the council members will continue to speak with Araeneve in private, while the Azelf and other council member form another group to greet the ball of light.  In the background of the human conversation, they will speak of daemonic interests to her through it - their excitement and worry and curiosity.  

The humans express their gratitude for the help, and their surprise at the lack of daemons.  She does seem normal enough other than not having a visible soul, but it's still a shock.