[That is a lot of White Amur (grass carp). Did you stock the sterile (triploid) type of carp? Hopefully they are not breeding in your pond. If so, then you may need to come back and start a new post about that potential problem.]
Hybrid black crappie will probably spawn in a 3-acre pond, but much less successfully than either black or white crappie. However, even "poor" crappie spawns can create a lot of fish in the pond in just a few years. Especially without a large predator to eat the brooder crappie.
Lots of people north of you have very nice ponds with the YP/RES combination with SMB (like Theo suggests). However, a quick search of fish suppliers near you did NOT show any that carry SMB, which suggests you may be out of their best geographic range.
You might be able to get by with just a YP/RES pond, since those two species can both be either forage or predator. You will need to catch some YP from your pond as they grow larger. They are quite tasty! You should also deliberately fish for your RES every now and then just to sample their size and health.
With close to zero plants, your FHMs will be eliminated in a few years. Now might be a good time to stock some Gambusia (mosquito fish), they are more elusive than the fatheads, and would reproduce well in your pond if they had suitable habitat. (Some suppliers in your area do carry gambusia.)
You could put in largemouth bass and crappie. However, that is a tough combination to keep in balance in a 3-acre pond. You could go crappie and no larger predator, but I think you would probably gets lots of stunted crappie without a breeding source of abundant minnows in the pond to feed them.
You could try a "bonus" fish like hybrid striped bass. Stock just a few, and they will grow large on your forage fish, but will not reproduce in your pond.
For a really clear swimming pond, you could even stock some tilapia. The eat filamentous algae and should grow very rapidly in your warms waters. They will even eat pellets. They are somewhat catchable with hook and line. In cooler waters they die off over the winter and people re-stock the next spring. Some of the fish suppliers in your area do carry tilapia. You might call them and ask how their life cycle would go in YOUR pond conditions. There is a chance they would survive most or all of the winters in your location?
Personally, I would want to add some artificial cover to my "swimming pond" to create more habitat for fish, even though they are the secondary goal. After the kids get bigger they may graduate to kayaks and paddle boards around the pond. Adding structure in kayak areas is not a problem, but beginners fall off of paddle boards a lot. Can you designate a few "no go" areas in the pond if people start doing recreation activities outside of the main swimming area?
If so, I would read some of the archive section for cover. It will really help your minnows and also greatly benefit the YP and RES.
Pond Boss - Cover ArchivesHave fun improving and enjoying your pond this year!