How did Rune make it from the Esper Mansion to Motavia? Even with Ryuka, you can only travel within the planet you're on, and he didn't have a spaceship.
We don't know that for sure. Lutz had his own cryo-chamber independent of Mother Brain in PSII; it stands to reason that Rune may well have had memories of Algo's ancient technology and where to find the old installations, which we already know are capable of autopilot (like the shuttle that Demi gives you just after beating Zio), and how to get himself to Motavia.
In PSII, Shir also manages to pull off the same trick if she runs off on Dezoris.
While we talking about crazy teleportation tricks, Lutz has little difficulty zipping the party back and forth from Noah. It looks like long-range teleportation is in the Esper bag of tricks, even if it's not in Rune's or Kyra's personal repretoires.
See Gameplay and Story Segregation. Rune also displays the ability to do a megaheal on Chaz (restoring all HP/TP/Skill charges) during part of the story, but in actual gameplay can't even cast a lowly Res-spell.
Maybe it's something he can only do when he's in the Inner Sanctum and close to the Telepathy Ball?
The Esper Mansion also seems to have access to the "Dew" perfumes; maybe he's using those.
Another possibility is he DOES know the spell and is capable of doing it when he needs to, but is unable to take the group with him, or it takes a lot of energy and he needs extra time to recover, or some combination. Basically, he can if he needs to, but it's just impractical and the spaceship is more reliable or straight up necessary for the whole group.
Fanon holds that the Ladea Tower has something to do with Rune's interplanetary travel.