Ban appeal board will be good but I think it will only increase ban appeals though it can be grouped.
With the ban sub board, it cleans the meta and should make it easier far the mods/admins to sort them out. If it's only temp. Bans it shouldn't be queried at all, you're getting your account back one way or another. Permanent Bans should be able to be queried in that section.
However it's up to the mods to leave the notification, and when I move threads, I don't leave moved notifications everywhere. I don't leave behind a moved notification if the forum thread has had no responses yet since only the opening poster is likely to care about the thread so far and they should already have the thread on watch/subscribe.
If it can't be removed all together, there should at least be a feature to hide moved threads provided by the forum.