What the brief does is pretty much implicitly acknowledge that Kellum has to fall for McDaniel to win. The case at its core turns on whether McDaniel convinces the Court it is wrongfully decided– is it wrong to read the statute as if it had a deadline. While I’ve seen cases (one an election contest!) decided by the Court overruling a clear precedent, I’d predict against it here.
There are couple of new themes. The brief opens with three pages attacking the state Republican executive committee for not doing its job in a timely way, but does not really tie that into the main argument. It closes by responding to the Cochran brief argument that the issues raised only by amicus cannot be reached by the Court.