All-righty, I've done a bit of thinking here. Just a bit.
Squad 5 and Squad 1 do not cancel each other out. I see Squad 1 as the ultimate authority that has watch over all of the squads and sort of encompasses all of them. Yes, all of the records are filed at squad 1, but squad 5 can collect and categorize all of the information.
Squad 13, Reave said long ago, is communications. They deal with the whole hell butterfly whatnot and perhaps the dangai. And might as well include Nix's artifacts on the side.
Now, for the two empty squads... either 4 or 12 could take this role.
One would be the janitor squad, but with a twist. Yes, they clean everything and whatnot, but they also have keys to everything. They could be a secretive security division that keeps a watchful eye on the seireitei and reports suspicious activities to the other appropriate divisions.
And for a few ideas the other one could take:
-Some sort of economics division that handles the distribution and costs of goods, handles shinies, taxes, etc. (this one look like it'd work the best)
-Head of the Shinigami Academy, a sort of educationy thing
