Of course a Gnome can sneak in there. Arborea is an outer plane you can just plane shift there if you don't use the portal to it's first layer of Arvandor. So yeah the Gnome could go there and I doubt the Elven Gods would have problems with him being there. (Evermeet meanwhile would have a problem as it is an Elves only place. The main branch of the Elven Supremacist Organisation lives there even.)
So we seem agree on this point: you don't need the permission of the elven gods to get to Arvandor via Evermeet. Canonically, creatures have snuck their way in. So when you say this:
And just to tell you won't be welcome in Arvandor unless you worship Elven Deities. Because Arvandor is the domain of the Elven Pantheon, and they have the right to bar anyone from being there if they feel you should not be there. So no you still need the gods for heaven.
That's not really the case. You don't need the elven gods. You can get there if you're sufficiently clever/resourceful/
adventurous/etc.
The point where we disagree seems to be this:
But he would not stay in Arborea when he died. His soul would go to the Fugue Plane like everyone else.
There doesn't seem to be any direct support for this hypothesis. Evidence against it includes the 5e DMG's rules for how the afterlife works. The SCAG seems to modify this general state for FR, but there's no implication that it holds weight on the multiverse beyond Toril. Given that FR has always been canonically part of the greater D&D multiverse, the most logical reading would be that on Toril, things work according to the FR rules, and off of that world, things work according to general D&D rules (other worlds may have their own local exceptions). If Drizz'zt boards a Spelljammer and goes to Oerth and is killed by a monk of the Red Brotherhood, does he go to the Fugue Plane? Or would he be subject to normal Greyhawk death rules? If Elminster was shot in a drive-by while hanging out at Ed Greenwood's house, would he go to the Fugue Plane? Or would he be subject to whatever metaphysical rules dominate here in the Real World? (Curiously: if the afterlife works like it did in Dante, Elminster would likely be damned to hell as a pagan, and Ed's first concern should've been sharing the Bible with him!)
Where Canon is silent (as it seems to be here), the needs of the Story can dominate: Toril as a prison for souls is an entirely consistent reading of the setting, and serves the Story we're telling here by creating a compelling and omnipresent antagonist for the heroes to fight against, a bad situation that heroes can change.
He can pursue Justice by tearing down Kelemvor's wall himself, acknowledging the injustice of such a thing. Otherwise, he's not really a god who cares that much about justice, apparently. Or he cares about his own hide more than he does care about Justice. Which makes him kind of a failure as god of justice, in the end. It'd be like being the god of semi-automatic firearms that shoot delicious chocolate bunnies: you're the god of something that ultimately doesn't exist.
As for the justice of the wall. The guy has days to years to say "Hey Tyr take me in." while in the fugue plane waiting judgment. If he does not then he is a fool honestly. The rule is you go in the wall if you reject the gods, you may not like it or consider it just but it is the rule. Many of the Gods including Tyr probably don't consider it just. But it is outside what they can do and for the most part considered a necessary evil.
One of the thins that people care about when they care about justice is the
principle. It doesn't matter if the bar for entry is ridiculously low, it is unjust to have such a bar in principle. A god of Justice should be
very concerned about this "necessary evil" that is not actually apparently all that necessary, since it was put in by a thinking being for a purpose.
Even if the Wall did not exist or he had faith and just went unclaimed for some reason (Which considering his personality would be very unlikley). He would not go to a paradise. He would just be put in the bleak city of the dead with people that share a similar outlook to him.
That suffering is the first circle of Hell in Dante. That's still a punishment for a soul, to be eternally deprived of a paradise that, by all accounts, they should be open to, if there was justice in the afterlife.