Back40, I can't speak for the group and their motives, but my guess would be that they are attempting to wage a small, but realistically winnable battle, and that they are hampered from filing a suit like the one you describe, because of limited funding.
Key members of the 1934Group are also pushing hard for a new NFA registry amnesty, which could potentially result in thousands of newly transferable full autos being available to the general public.
Again, I think they are picking fights that they think they can win, and while these might seem like insignificant steps to some, I agree with their strategy of building legal momentum through a series of small, attainable victories.
Just think of the financial support and exposure that they would receive from the general shooting community, if they succeed in slaying the Federal dragon on both accounts.
Then it becomes time to tackle things like the 86 ban, and even the National Firearms Act itself.
Rome was not built in a day.