By the way, here's the relevant section that, to me says that Byrd CAn sign a long term deal with another club:
(k) Any Club designating a Franchise Player shall have until 4:00 p.m., New York time, on July 15 of the League Year (or, if July 15 falls on a Saturday or Sunday, the first Monday thereafter) for which the designation takes effect to sign the player to a multiyear contract or extension. After that date, the player may sign only a one-year Player Contract with his Prior Club for that season, and such Player Contract may not be extended until after the Club’s last regular season game of that League Year.