Hmm, have you looked at the WarChanter PrC from CW? It doesn't progress casting or Inspire Courage, but it has full BAB and various alternate songs that fit with the Metalocalypse theme (some are really quite good - its capstone gives all allies within 60' BAB equal to your character level). Losing casting progression hurts, though.
For inspire courage, be aware that without Words of Creation it won't be as impressive (and roleplaying working with the Drow while being exalted is unlikely to go well). With the right items you can still make it work, though.
Note that becoming a dragonborn requires you to be non-evil, and being a servant of Bahamut may cause some RP issues.
If you have access to Tome of Battle, Bard pairs very nicely with Warblade or Crusader. You can take a feat (Song of the White Raven) to allow your Bard and Warblade or Crusader levels to stack for the purpose of Inspire Courage. Your casting will suffer, but you can supplement that with maneuvers.
A few options:
Bard 3 / Fighter (or Barbarian, Paladin, any Full BAB class really) 2 / Warchanter 10 / X 5
(ending with Bard 2 / Sublime Chord 3 gives you a little late game magic, but probably comes too late to matter [edit]: Whoops, you don't qualify for Sublime Chord)
Key feats:
Combat Expertise and Weapon Focus (prereqs for Warchanter)
Dragontoched (if you're not going Dragonborn or if you want to change your DFI damage type)
Draconic Heritage (if you want to change your DFI damage type, requires Dragontouched even if you're a Dragonborn)
DFI
Lingering song
Can use two songs at once.
Inspire Courage of 2 (effective bard level of 8 with Vest of Legends) + 1 (Masterwork Mandolin or Natural Horn Horn) + 1 (badge of Valor Item) = +4 to-hit / +3 untyped damage or +4d6 fire damage (or you can do both in the one action, but you'd be better off using inspire legion + DFI).
BAB = level - 1 until level 16, but then you can use inspire legion to give yourself (and your allies) BAB = your level.
Only first level spells until level 16. (ie VERY weak casting)
Bard 4 / Warblade 16
(you could also go Crusader, but their withheld maneuvers mechanic can be annoying)
Key Feats:
Song of the White Raven
Dragontoched (if you're not going Dragonborn or if you want to change your DFI damage type)
Draconic Heritage (if you want to change your DFI damage type, requires Dragontouched even if you're a Dragonborn)
DFI
Lingering song
BAB of +19
Access to 9th Level maneuvers.
Inspire Courage +4 (Bard/Warblade) + 1 (Mandolin) +1 (Badge of Valor) = +6 to-hit / +5 damage or +6d6 fire damage.
No need for a Vest of Legends (save 16,000gp).
Able to cast 2nd level spells.
Bard 8 / Virtuoso 2 / Sublime Chord 2 / Virtuoso 8
(if you have access to Tome of Magic, taking a 1 level dip in Binder will let you take 10 on Diplomacy and Bluff checks, which works well with your high CHA)
(Bard 9 gives you inspire greatness, Virtuoso 10 gives you mass true seeing with a use of your bardic music and lines up better for BAB and saves)
Key Feats:
No feat prereqs
Dragontoched (if you're not going Dragonborn or if you want to change your DFI damage type)
Draconic Heritage (if you want to change your DFI damage type, requires Dragontouched even if you're a Dragonborn)
DFI
Lingering song
Very strong casting, although it doesn't take off until mid-high levels.
Creaking Cacophony (level 3 Bard and Druid spell from the Spell Compendium) grants sonic vulnerability (+50% DFI damage)
Total of either +11 or +12 BAB, depending on how you build it.
Inspire Courage +4 (Bard/Virt levels with VoL) + 1 (Mandolin) +1 (Badge of Valor) = +6 to-hit / +5 damage or +6d6 fire damage.
