I've played a number of older J-45s that had the tonal quality that you are seeking, and I've played a number of older ones that did not (they exhibited the thuddy character without much sustain mentioned above). The same can be said for newer J-45s that I played.
I skipped over a number of newer examples because I just don't care for the thud-like bass with no edge on the note and no sustain, just personal preference. I ended up with a 2008 J-45 TV and love the low end on this guitar. Here's a sound clip of the guitar:
Walking Nick