UVA, UNC, GT, and KU are all AAU members, VT and FSU are not. AAU membership isn't all it's cracked up to be though. VT and FSU are ranked academically higher than KU. In fact, out of all these schools, I think KU is the only one that might be disqualified purely for academic reasons.
KU is honestly not that bad...they're slightly better than Missouri, at any rate.
FSU isn't an AAU member, but I had found a few documents recently illustrating that they're actively trying to obtain AAU status.
As for Nebraska, I've heard that unless new leadership takes hold of the AAU and reverses the trajectory they're on, we won't get back in, and more ag research schools will be purged. Don't know if that's still the case, though.
Yeah Nebraska isn't getting back into the AAU and I am pretty sure after how the whole thing went down the administration isn't big on going back either. Syracuse even left the AAU on their own will because they were about to be pushed out.
That said anyone paying attention to Nebraska academics will see they are making big investments on that front. Nebraska will be ranked last in the conference for a while, but in another decade UNL will be much closer to the pack than they are today. Innovation Campus is going to be huge.