For the full disclosure I like the open tone of the A-Bomb or Rebel Yell.
If you're looking for "fuller/fatter" as described in your first post, the HD will certainly fit the bill--but it just wasn't for me in the long run.
I had a Holy Diver in a Strat with similar specs (alder body, maple neck/rosewood fb, bolt on, 25.5" scale) and found it too thick and chunky. Couldn't get it to open up enough no matter how I tweaked the EQ or opened up the tone knob. It just sounded too fat. Single notes sounded really good and buttery, but the chords felt way too thick.
I had it for about a month or two and ended up replacing it for an A-Bomb. I'm much happier (albiet it's not as aggressive as the A-Bomb I'm used to).
My vote is for the Abraxas since you don't want something too "raw punk hairy" but more of something smooth.