No worries on the head unit, however you should defo upgrade those old Toyota speakers, as compared with the JBLs (or any other quality car audio speakers) they'll be piss poor and almost certainly (mostly if not wholly) responsible for that "bright or busy" sound you mentioned.
You have to remember that pretty much anything audio-related that comes as standard in 90% of cars, costs pence to make, rather than pounds - and it shows!
Marco.