Wish I had caught this thread a while back.
I too recently bought a 2013 Elantra but not with the "better" Navigation head unit, just the standard blutooth enabled unit. Frankly, I think the sound system is pretty mediocre, at least in the standard Elantra, *especially* the speakers. You mentioned yours had 6 speakers - were you talking about four 6 1/2's in the four doors and 2 tweeters in the top part of the front driver/passenger door panels? I ask because the way the rear window/trunk panel is constructed, there's no easy way to get any exposed speakers in the back unless you have enclosures custom made.
I pulled my entire system out of my old car and am in the process of figuring out if I can get it into the Elantra. It includes:
4 Focal 165 V1 speakers (one 6 1/2" woofer, one 1 3/4" tweeter per )
Alpine 12" subwoofer SWR-12D4
Alpine 4 channel Amp MRP-F600 (speakers)
Alpine 1 channel Amp MRP-M500 (sub)
Alpine CDA9887 Head Unit
I will likely upgrade the head unit later and probably with something a bit nicer than the Alpine 9887(which honestly is an outstanding unit regardless), but there's the cosmetic issues getting any new head unit single or double din to elegantly sit in the dash panel, not to mention the hassle of integrating any new head unit with the steering wheel controls.