The capacitor would be wired in series on one line, thus storing the DC for the speaker's use

That won't work. A cap blocks DC current (after having charged up to the supply voltage)

You need to wire it in parallell to the power supply and the speakers (ie the + lead [supposing a polarized cap] to the +wire from the supply (which then continues on to the speakers) and the - lead to the -wire from the supply (which then continues on to the speakers)

/Michael