The typical bard can use the bardic music effect inspire courage to grant allies morale bonuses on attack rolls, weapon damage rolls, and saving throws against charm and fear effects. A bard with the feat Dragonfire Inspiration (Dragon Magic 17–18), instead of using the bardic music effect inspire courage to grant morale bonuses on attack rolls and weapon damage rolls, can use the the bardic music effect inspire courage to grant allies extra d6s of energy damage equal to what those morale bonuses on attack rolls and weapon damage rolls would've been… and morale bonuses on saving throws against charm and fear effects, too.
Can the bard that possesses the feat Dragonfire Inspiration do the following?
Round 1: Take a standard action to spend a bardic music use per day to employ the bardic music effect inspire courage normally. End the bardic music effect inspire courage; this is not an action. Note: The effects of the bardic music effect inspire courage nonetheless persist for 5 rounds after the bard's ended it.
Round 2: Take a standard action to spend a bardic music use per day to employ the bardic music effect inspire courage, this time employing the benefit of the feat Dragonfire Inspiration to grant allies the feat's benefit of extra d6s of energy damage, the morale bonuses on saving throws against charm and fear effects overlapping with the existing bonuses.
In short, is it legit to spend two uses of the bardic music effect inspire courage on different actions—ending one before starting the other—so that the bard and the bard's allies get both the normal benefits of the inspire courage effect for 5 rounds and the modified-by-the-feat inspire courage effect for as long as the bard maintains it?
Note: While to this reader this seems reasonable—both from a balance perspective because of the resources that must be devoted to it and the actions it consumes and from a purely mechanical perspective because the bonuses overlap rather than stack—, a player new to my campaign asked about this interaction, saying that the interaction's hotly debated and perhaps even, ultimately, can only resolved by a DM's ruling. Maybe my inner rules lawyer is holding me back, but I'm especially unable to muster any arguments that would disallow it, so answers from both sides are welcome.