Now for some more direct comments on the actual text… 
1.) It’s a very nicely thick and compact NT exegetical case; with a good selection of OT side-references for principle.
2.) While I might complain a bit about the visual presentation being rather flowery (as far as fonts, italics, different justifications–not to be confused with the theological term 
--etc.), the varied visual look can help readers who have trouble following dense paragraphs. And I don’t mind the concurrent rhetorical flourishes, so long as the underlying material is substantial and sound; which is true in this case. (I don’t like seeing rhetorical form substituting for substance. But that isn’t the case here. 
)
3.) While I know the standard interpretation of Rom 9’s vessels of wrath and mercy involves them being the objects of God’s wrath and mercy (which admittedly has definite relevance to the original context of the quote about the Potter/pottery and answering back to God–and which original OT context is very importantly universalistic!), I find that the larger narrative/rhetorical context rather involves the notion that God creates some vessels to pour out wrath and some to pour out mercy. St. Paul may be combining the two analogies here in chapter 9, but this other analogy has an important role in the rhetorical thrust of Paul’s goals up through chp 11 (at least), that shouldn’t be (but almost always is) ignored. Namely, his Jewish and Gentile audience shouldn’t be busily blaming each other and claiming the moral high ground in regard to persecutions and failures by the other side. Jews and Gentiles both have served as agents of wrath on each other, and not always in an ethically approvable fashion; but God is incorporating all that into a winning scenario for everyone, in the long run.
This certainly doesn’t re-introduce a non-universalistic element to the reading–far from it! 
But, that should be another reason to keep it in mind during an exegetical case.
4.) Back to discussing the application of terms translated “eternal”. I’m afraid there’s a bit of a category error in trying to claim that because Heb 6:5 refers to “the impending eon” {te mellontos aio_nos}, therefore the adjective “eonian” in regard to the chastisement of the goats in GosMatt means the same thing. The words are obviously related, but are not the same terms. In fact, what makes {aio_nos} mean ‘pertaining to the eon’ in the first case, is its explicit reference to the age that is about-to-be.
This doesn’t necessarily hurt your case, but it does leave you open to a possible non sequitur complaint.
5.) In point of fact, {aidios} doesn’t mean unending. It means imperceptible. Thus the Rom 1:20 ref you cite reads, “For His invisibles [hard to translate that term , but probably means something like invisible attributes] are descried from the creation of the world, being apprehended by His achievements, besides His imperceptible power and divinity.”
The word is only used twice in all the NT (so far as I’ve been able to find. Anyone else…??) And, to be honest: the only other time it’s used (that I can find) is in reference to the imperceptible bonds of the rebel angels God has imprisoned “under gloom” for the judging of the great day. (A reference found in a paragraph reminding readers how the Lord Jesus (!) destroyed those who, like Egypt, believed not, including Sodom and Gommorrah who are “lying before us, a specimen, experiencing the justice of eonian fire.” 
)
So… um, yeah, despite your claim, it is in fact used in half its NT references (such as those are ) to refer to those in hades and/or Gehenna; and in fact its particular use in the epistle of Jude connects directly not only to the concept but to the word ‘hades’ itself meaning ‘the unseen’. (Even though ‘hades’ as a term isn’t used there.)
Fortunately for you, though, it doesn’t actually mean ‘unending’. 
It picked up that meaning as a bleedover from what people guessed the implications were of the Jude paragraph, I suspect. Or (maybe more likely, though not discounting that other explanation as a factor) because at a fast glance it looks a lot like an aion- cognate. But it isn’t.
So it’s a compound error that definitely needs correcting: aidios has nothing to do with duration (endless or otherwise), and is in fact used in regard to hell. But the corrections make your case better, not worse. 
6.) Actually, we do see some highly (even crucially! ) important outgoing traffic, in the final chapter of RevJohn: the river of life (a symbol for Christ) going out from under the throne of God, into the lands where those who continue to love their sin are living. Moreover, the saints are exhorted by the Spirit (Who also may be thus said to be going out) to join Him in exhorting the currently impenitent to drink freely of the water, slake their thirst, wash their robes, and thus obtain permission to enter the city to be healed by the leaves of the tree of life.
You do mention the Bride, briefly, inviting the deceived to be saved; but the super-important piece of the picture is the river of life flowing out of the never-closed gates.
So, again, a correction (strictly speaking), but it makes your case vastly better, not worse.
7.) The quote from John Stott is poignant; but it in a backhanded way it actually hurts your case. Stott, last I heard, is still an annihilationist who thinks that living with the idea that God hopelessly punishes sinners for a limited period of time and then wipes them out of existence, doesn’t require “cauterizing” his feelings about the final fate of the sinners. Insert irony here as applicable… 
Unless he’s actually “Gregory”… Which would be unbearably cool. But still, less than helpful for your paper as things currently are. Unless he became an open universalist, and I haven’t heard about it? (Entirely possible. Just asking.)
(I will mention here that a former pastor of mine recently started switching to annihilationism thanks to John Stott, whom he was amazed to find holding the belief. We used to dialogue on universalism vs. non-universalism over pizza once a week for lunch, for a while. Some of the best hours of my life, that year.)
Despite my crits, I actually think pretty highly of the compact density of the case you’ve put together there. It’s good work and good material. Needs some tweaking in places; and I don’t know that it really directly addresses the question of why we should interpret apparently non-U verses in light of apparently pro-U verses instead of vice versa. One can state that it’s a raw choice of whether to choose in favor of hope or not, but that leaves you at an impasse since the other side can do the same thing in the other direction with just the same amount of justification.
Which is why I insist on appealing back to a set of beliefs that we’re supposed to be sharing in common with the non-universalist orthodox Christians: namely, the orthodox theology! Even though that leads into greater technical complexity, it provides a common standard of agreement (ostensibly anyway) to be advancing from.
But: for people who clearly want to hope but don’t yet see scriptural ground for doing so, your essay succinctly and thoroughly brings forth very many good and important scriptural grounds for hoping that all may be saved. I’d be honored and pleased to make use of it myself–with some tweaks as noted above. 
)!