My main issue is, as was said, River Shoulders would be a noticeable physical figure. Now, he could have been shape changed, but why, other than to hide his identity from Harry, the only person who would know of their connection?
Also, he's not really shown up much as a character in the main series, so I don't really think Jim would throw a character we've only met in short stories into such a role in the main books.
Given that the Circle/Black Council is suggested to include more than just strictly mortal wizards (Probably a denarian, probably some vampires) it wouldn't be out of the realm of possibility to include other flavors of supernatural forces on the Grey as well.
I wouldn't expect to see Gard as one of the 13 though, either. I don't see anything that she brings to the table that Odin doesn't, just more of the same, and having a subordinate like that basically gives Odin 2 votes rather than 1 for any kind of democracy they do.
Luccio and/or Ramirez would also be good candidates, I would think. Only question is whether or not they'd be able to slip away and make it to the fight.
Also, someone with the books handy can probably double check me, but Lea and the Knights are very definitively out of the running, yes? Already there when the rest of them showed up to make 13.