I considered that new Warchanter song earlier and
recommended against it. It would widen the melee DPS gap between Warchanter and non-Warchanter groups too much. Imagine if today the Haste cast by a Warchanter gave 10% more attack speed than other Hastes... that would be excessive, right? But that's rather what a Doublestrike song could do.
Here's a bit of elaboration on it. The naive way to make a Song of Doublestrike is for it to work like a regular bardsong with the same 3-6 minute duration, and for it to give a +10% increase to Doublestrike. That'll mean 10% more DPS from THF/S&B guys, 5% for STWF guys, and in between for other types of TWF builds. That could be similar results to a stacking +8 damage song, which is clearly very powerful and would have to be the primary benefit of Warchanter 2 or 3. But if they reduce the Doublestrike bonus to 5% or something then the song doesn't seem fun anymore, because players rarely ever notice it triggering.
So a better approach is to make it a bigger doublestrike bonus, but with a lower uptime (duration/cooldown ratio). That means that whenever the Warchanter uses it everyone can see the power boost, but he can't keep it going enough to be really imbalancing. Maybe something like this:
Urgent Shout: cost 30 sp, duration 8 sec, cooldown 60 sec, casting time very fast. Nearby allies gain a temporary +30% doublestrike. (Metamagic cannot apply)
That version has 13% uptime, so the total effective mainhand boost is 4%. It would be only one of several new effects Warchanters get, so it doesn't need to be the main attraction.
Sure, all three bard specialties need help. The ones not related to melee attacks would be pretty offtopic here.