You got it right. I continuously feed ocellaris because they have to go through a metamorphosis. Banggais are more developed - by the time they use up their yolk sac they are functioning pretty well and have a huge mouth in comparison to their dinner, so hunting is easier. So no, I don't have food present at all times for banggai. Twice a day they get a good dose of newly hatched BBS.
My advice to you if you plan to keep raising the banggais, which you certainly should since you are so fortunate to have a pair that spawns: set up a very simple growout system. Get a 20 long with tank dividers. If you can plumb it to your existing DT sump or set up a good HOB filter/skimmer you will save yourself time on water changes. As the little guys grow they will need to be separated when they start to fight. In my experience keeping them in small breeder nets stunts their growth. My oldest one is small because of that. Plus a 350 micron mesh will need to be cleaned frequently and the water circulation/exchange could be rather poor inside the net.
Around my area (Twin Cities metro, MN) you can sell a CB banggai for $45 each and there will be a waiting line. You can sell them wholesale to a LFS who understands that Banggais don't ship well at all for $20-$25. So it may pay for itself to grow them out depending on your environs.