This is how I see it, but it is not any type of conclusion, just my opinion for comment:
The defendant did not lawfully possess the UZI on Sept of 1994 because after the date of his arrest in May 1994 he could no longer legally possess firearms. Part of the conviction was later overturned, but because he was not in lawful possession in Sept 94, he could not get it back.
The question turns to: Who possessed the UZI in Sept 94? The defendant or the Gov't? Really we see the point is moot, because if he owned it, it would be illegal since he was now a felon. If the Gov't "owned it" (because they possessed it), than on Sept 94 he didn't, and he cannot get it back. Neither could his brother as agent.
He tried to have the court give the weapons (there were 4) and ammo back to his brother as a designated agent. Three weapons and the ammo were returned to his brother, because they did not fall under the AW Ban, or they remain legal (Mossberg 12ga). The AW Ban seems to state that only AW's LEGALLY owned in Sept 94 were eligible for the grandfather clause. Again, since the defendant did not LAWFULLY possess the UZI at that time, it became an illegal firearm under the AW ban. The other firearms remained unrestricted and were returned after the conviction was overturned. They were returned to his brother, as his designated agent, because the defendant still had other criminal convictions making it unlawful for him to possess firearms.
A criminal possessing an UZI in Sept 94, cannot claim that it should be returned under a grandfather clause which only applies to LAWFUL possession on that date. Despite having the conviction later overturned, he did not possess the weapon legally, because he continued to have felony convictions that were not overturned.
If he had all his convictions overturned, then on Sept 94, despite not having possession of it, the court may have seen him as the legal owner on Sept 94 and it would have been returned and transferable. The court does not go into the technical possessor of the weapon, only that since he wasn't, he couldn't transfer it to his brother.