I’m assuming it wouldn’t be cheaper just to buy some nano brine from algae barn?
It's very cheap and easy to hatch them yourself and you want to have a steady supply so you never run out so I highly recommend you start a BBS culture. And I would also recommend starting it 3-5 days before you think he's going to release(or more, I never stop, it's just a part of my tank chores now).
(My live food setup, the 10 gallon was holding tank for blackworms for my CBB)
You can always feed the BBS to the tank before the fry is released, your fish and coral will love it. It's also important to note that BBS alone is not the best source of nutrition, copepod nappuli are probably the best but you can also enrich the BBS with Selcon to increase the HUFA's in them which will in turn decrease sudden fright syndrome occurrences and should dramatically decrease or prevent mortality from those instances:
https://drive.google.com/file/d/1hXE2jk60_3MFUBvYZnlG3CGrRREIhy7B/view?usp=sharing
I've been breeding Banggai Cardinals for a couple years now, IME the male will hold the eggs anywhere from 23-30 days. My breeding pair are just in my reef tank so it can be tricky to retrieve the fry before they get eaten by the other fish or sucked down the overflow. So my strategy is when the male is close to releasing I put in a bunch of fake sea urchins I made and remove mechanical filtration as well as making sure all pumps have foam guards to prevent fry from getting sucked into pumps, you'll know he's close because you will see the little baby fish trying to push their way out of the male's mouth in the few days before he lets them go. The fry will tend to go to the sea urchins and especially the ones in lower flow areas. So it makes it so the other fish have a much harder time getting to them and groups them together for you to easily collect them. On several occasions I've turned the flow off and been able to just slowly lift the sea urchin up and the fry will travel up with the urchin, then I just put a net under and lift them out. Easy.
(Fry peaking out from my male's mouth)
(Fake sea urchins made of epoxy and zip tie clippings)
Then I check just after lights out, middle of the night if I'm up, and first thing in the morning every day until they are released. Also, it's common for them to release over the course of a couple or a few days so don't assume he's empty until you see him eat again. As he releases them I snatch them up with a small net trying to damage a few corals as possible, some damage is inevitable in my tank it seems. And I put them into either a breeder net or a Tupperware with slits cut into it, just enough to provide some flow but not large enough for them to escape. I keep them in there for the first couple weeks or so before transferring to a 10 or 20 gallon of their own. Right now I've been growing them out in my little frag tank. Eventually they will mature to a point where they will start to pair up and try to defend a territory so they will need to be separated but I'm usually able to get them eating frozen foods and get them sold off before that happens. Here is a link to a good paper on breeding these fish if you're interested in reading more:
https://drive.google.com/file/d/1j2GkAVjV690otY8dKC28GefArIxpWMT6/view?usp=sharing
(Latest batch in a Tupperware that is also home to the baby fungia corals my fungia skeleton is giving off. It's cool seeing the corals and fry all eating up the BBS when I add them plus my pistol shrimp is a thief so they're safe up there)