Not exactly an ideal solution but this is what I'm doing for now. Core box holds the 2 boards, tokens (in bags), rulebook, and all the cards are inside of binder sheets. I carry 2 loose 1/2" Avery binders that I can quickly just stick in the binder pages for whatever matchup is being played.
I originally tried to put the Codex binders I made into the Core box, all starter decks into the Starter box, and all Tokens into the Flagstone vs Scourge expansion box. It mostly worked but the Core box won't fit the next two binders with cards once the last expansion comes out.
I also found that the lid would not close with the binders fully loaded. So I took out the heroes and starter deck and put them in the slots which I assume is for Bashing/Finesse/Tokens and then the list closed OK. Not quite flush with the bottom, but acceptable.