Inspirational Stacking?

[Siuis]

Works best at low levels I guess, bt I'm looking at two things in particular. One is that an unmodified bardic music effect lasts for an additional 5 rounds before expiring. The other is that Morale bonuses don't stack for the same thing. But can they "stack" for different attributes? Say, a different buff for AC and saves.

More specifically. A bard3 with Song of the Heart, a badge of valor, and the inspirational boost spell has an inspire courage total of +4. If I throw in Dragonfire Inspiration, can I;
Use inspirational boost, and sing to grant +4d6 energy damage;
Use inspirational boost and sing for +4/+4 attk/dmg;
Fight for the next four rounds with +4 on all attacks and an additional +4d6 +4 to damage

Or do i lose the +4 to damage, since it is the same as the +4d6 and they overlap rather than stack?

I'm really not sure how to rule this one. Any help is appreciated!

 

[parinho7]

with dragonfire inspiration you can choose to lose the +4 on attack and damage rolls that you normally have and instead deal +4d6 points of fire damage

From Dragon Magic:

Each ally so inspired loses the standard morale bonus on
weapon attack rolls and damage rolls. Instead, he deals an
extra 1d6 points of fi re damage with his weapons for every
point of morale bonus that your inspire courage ability would
normally add to the attack roll. For example, an 8th-level bard
using this ability would add 2d6 points of fi re damage to his​

allies’ attacks.

 

[Siuis]

Yep. Bt bardic music itself states that once you stop performing, the effect continues for another five rounds.
Now, during these five rounds, If I use inspire courage again but this time I choose not to use dragonfire inspiration, that gives me:
4 rounds of two bardic music effects
1 round of only the second bardic music effect

My question is, do they stack or do they overlap. I can see how dragonfire inspiration would say you forfeit normal inspiration bonuses... But it reads more like an "instead of he normal function" clause.