Distortion in the bass is often a problem with stock headunits and amps, although it's hard to tell exactly without hearing it for myself. I would personally replace the whole system, everything from the headunit, to the amps, and to the speakers. You'll be able to customize it exactly how you want it, and upgrade it if you want more and better sound.
2003 Mustang GT
Intake & Exhaust: K&N FIPK CAI, Mac O/R H-Pipe, Custom Catback w/ Magnaflow Magnapack Mufflers.
Suspension: H&R Super Sport Springs, KONI STR.T Shocks & Struts, J&M Caster Camber Plates, Steeda Bumpsteer Kit, UPR Elite LCA's & UCA's.
Performance: BAMA 93R Custom Tune, FRPP 4.10 Gears w/ Terminator spec T-Lok.
Planned Mods: FLSFC, Eibach Sway Bars, Throttle Body, Plenum, Rims.