Are you looking to make playable CDs or just to store the music? If the latter, burning onto DVD-R's would be an option, they hold around 7 times more data than an ordinary CD. If the former, I doubt there'd be anywhere that would do that, plus how would you get the files to them in the first place?
As for the stuttering, it might be down to a dodgy CD- could be worth trying with another brand or burning at a slower speed.