That's assuming they were "passing through" (note the didn't say "crossing") parallel to the orbital plane of the planets. But it's not specirficed that the direction they came. They could have been passing through perpendicular to the orbital plane in which case "passing through" would take significantly less time. Unless you are counting the oort cloud which is spherical in which case they would have to be traveling 100 times greater than warp 9.975. So I think it's safe to say including the Oort cloud it out.
Truth be told they probably were "passing through" at some oblique angle.
We have the ability to detect gravity waves, but we can't generate them. So for the Vulcanians, perhaps they had some mathematical models of what a "warp drive" would look like. Then when they detected signatures that matched what their theoretical models predicted, they decided earth was of some interest after all.
This explanation would be a passable workaround for the "15 minutes through the solar system"-line. But my major grief with it still is: They Vulcans (which are on all other accounts more developed than us "primitive" humans) have only a time window of 15 minutes(!) in which they are in scanning range of the Phoenix' warp jump.
Whether the Vulcans scanned the gravity waves, or the EM-emissions from the warp jump, all those travel with lightspeed omnidirectional from Earth orbit. The Vulcan starship
has to be faster than lightspeed to be able to escape that expanding event horizon in the first place.
Here is what I can give you: It doesn't have to be
much faster than lightspeed. Thoroughly possible that Vulcans were only capable of Warp 1 at the time, and on a huuge longterm mission (longer Vulcan lifespan makes longer space missions feasable). It actually really might be, that the huge "warp speed explosion" - more and more species being able for faster and faster travel - actually only came into effect
after humans joined the rank of warp-capable species.
But the writers' intent seems to be clear: Vulcans (and others) were already warp capable
before humans. Before that, they probably had their own little versions of the "prime directive", and thus not only ignored us, but also took further measures that we (and other species!) didn't know about alien life being out there, and were able to develop at our own speed, without being influenced by fear of other aliens or anything (thus also giving a neat explanation for the Fermi paradox -
https://en.wikipedia.org/wiki/Fermi_paradox). Only Chochranes first warp jump proved we are "ready" for first contact - like the Federation later will also use as a barrier for when to start diplomatic relationships with alien species.
Hmm. To me the line seems to indicate that they were planning on contacting the contemporary 1947 Ferengi. I don't see any indications of further time travel.
Well, all it proves is that Quark had a perception that Vulcanians had warp drive first. Which in my narrative is technically true since they did have warp drive, but then lost it centuries ago. So the reputation of Vulcanians having warp drive first is not undeserved. Though Quark clearly got his facts messed up.
Again, fuzzy memory, but: The time jump in that episode was induced by the Ferengi shuttle itself, not some outside disturbence, right? And they used that shuttle itself again to travel back to their time? For me, the line was pretty clear: "We have a shuttle that's a time machine. Let's get back to the time machine, and mess with history to our advantage". Otherwise the "centuries" remark would make no sense. Also, while I always am a big fan of "canon inconsistencies being explained by characters just being plain wrong about stuff" (like Chekhov's various "Russians invented that"-blurts), I think the general
order in which species arrived in te interstellar community might be basic enoug that even Quark is right there.
Also: Enterprise. In fact, your personal theory about humans being the first FTL-capable species is actually somewhat plausible (although I think it fits better in the Star Wars universe - where it serves as a nice explanation for the
total human dominance in that universe). But I think one has to view the
entire body of work of a franchise, and ENT pretty explicitly proved the generally accepted narrative of First Contact, with humans as being later than the other major players.
But the one thing where you actually made me change my mind is the speeds early Vulcans (and klingons, and Andorians) were capable off. They might have had warp speed already since a very long time (enough at least to develop century long histories of conflicts with each other), but the level of
technology - aka the speed they were capable off - those species might actually always not have been
that much ahead of us. And that only in the 22nd century
all major species suddenly had wide ranging break-throughs in speeds - humans always being only a small step behind the Vulcans, and soon the frontrunners, building their massive Federation.
Sounds like a reasonable explanation to me.
Thank you
Final note: I love how you consistently use "Vulcanians". They were called that sometimes during TOS if I remember correctly, right?^^
