Yes you can catch AJ on public spots, matter of fact since AJ like large structure, public spots can be the best, To get into the larger AJs you need to get into some deeper water, like the Marathon or Swingle Reefs or any of the rigs to the west in water over 200'. Rigs like the 252s and surrounding rigs can be a sure thing for large AJs.
As a rule if AJs are present they are easy to catch with either live bait or jigs. With live bait just use 5-10' of 80lb mono with a egg sinker above that is 4-8oz and use a large circle hook, drop 1/2 to bottom and hang on. I catch most of my AJs on jigs on reels loaded with braid, more fun this way to me! Just attach 3-5' of 80lb mono as a leader and tie jig to terminal end, let jig hit bottom and wind as fast as you can till you are 1/2 way up and do over till you get hit.
You need a reel with lots of power to whip larger AJs. I use Penn Torques and Shimano 20 and 30 Toriums, all with 65lb braid.
Hope this helps
2008 54C Viking "Jacquelyn"
2010 36 Yellowfin "Forgiven" (sold)
2010 24 Hurricane Deck Boat
2001 Contender 25 (sold)