The STI is a dang fine car but sure are noisy, I have personally deadened 4 of them and I hardly ever work on anybodies car besides my own! I do know what they need and when done so much nicer to just drive let alone listen to music.
If you do a very good job under the rear deck it will further reduce the noise level a significant degree.
The high level of noise from the rear is a major reason I developed the underseat subs for these cars, then you can really seal it off(there needs to be a passage for air for cabin vents to work properly, my STI guide covers that well) and have low noise, great audio, etc......and not much weight and all added between the axles, most of if down low, etc...does not effect handling much at all that way
Have a great day