Well if the GM and coach aren't going to be fired, it's probably time to have a players only meeting. Let the players figure it out, and if it means moving the C to someone else's jersey, let the players decide (the A's as well). And if there's a closed, players only meeting, I think it will become organically obvious who should get the letters. They may not be the players the team management and fan base would expect.
But if they did something like this it would possibly provide a demarcation point to the season in the absence of a coaching change or major trade.
And it would also (likely) be a hand-off of team leadership to the young core.