Octavia Combi Elegance - speakers and HU (Swing)

I recently bought a Combi 1.6TDI Élégance with the Swing radio/MP3 unit. I'm not exactly sure how many speakers the sound system has, but I'm suspecting there are 6 of them.

I'm not overly pleased (if not to say somewhat disappointed) with the sound quality. It's adequate for listening to jazz and classical at low (background) sound volumes, with the loudness option activated. But at levels more appropriate to appreciate the music (and keep my brain busy with something less monotonous than late-night highway driving), I find that the sound has an overly intrusive (stressful, stringent, aggressive) aspect, often making me want to kill playback of records I usually enjoy listening to. The tweeters mounted in front of the door handles seem to be the biggest culprits, but it could of course also be that there just isn't enough in the mid registers to flesh out the sound.

It may not be irrelevant to note that I have a rather good sound system at home, with a couple of Klipsch Reference towers in the final stage.

I saw (here) that the car speakers are much less to blame than at least the Stream radio, which has a bad reputation for quality. I haven't found an assessment of the Swing unit yet, though.

What is known about the different OEM speaker makes Skoda uses, and who makes the Swing unit? What's the best approach to improve sound quality with what's currently installed? I haven't yet found a neutral bass/middle/treble setting that works for most of my music, but maybe there are other settings that I should avoid (or activate)? I do turn off the Loudness at higher levels, of course, but it's much less clear to me what the Gala setting really does - or how to know whether it's on or off.