Big Al, yes I did wonder how "reliable" those soundtracks on the adverts are but, in fact , apart from the bass E the other strings do sound as good ,even without amplification, as the advert. Matt's solution is well worth a try, wouldn't you say ?
Supposing I was to change only the bass E string (for tension balance, perhaps the top E' also ) could that be a refinement of the solution that might work ?