LMB will survive, reproduce, and efficiently control BG in 1/2 acre. I see that occur many times in northern ponds and it will work anywhere in the US with management. I commonly see it successful for your intended goals. You won't have a lot of LMB and they may not get much bigger than 2-3 lbs with maybe the rare 4 pounder depending on how you harvest/manage the fish.
Your main 1st project is to learn what sizes and approximate numbers of BG that are present. This will determine what sizes of bass need to be stocked to survive the transplant. How are you sampling the bluegill? Only by observation? If yes go to WalMart and get a small pack of No.8 aberdeen thin wire hooks, a slender bobber. Buy no weights. The weight of the bobber and baited hook is enough to cast 20-30 ft. IF not you are doing something wrong. Get a small box of worms. Fish the baited hook with a piece of 1"-1.5 worm at various depths of 2 to 5 ft below the bobber within 10-20 ft from shore. HINT: if you all sit down while fishing, your catch success greatly improves. Measure every fish you catch and get some pictures of them. And keep track oh how many you catch in 1-2 hrs of angling. As a rule you should catch at least 20-30 per hour when sunfish are common/abundant. There will be a debate as to weather you toss or return the fish. I reserve my opinion until I see some catch information.
Your 2nd project is to verify with 1-3 pictures posted here of your "BG". We want to be sure you have BG and not some other sunfish.
My experience is if you are seeing a few(20) BG you likely have 100's that you are not seeing. If you have only a few BG then it is possible you have a predator/s thinning their numbers. This predator could eat small fingerling bass.
Your 3rd main project is to locate 7"-10" bass as stockers. Overton is a very good fish farm. Try to use them. They do have 6"-8" and 8"-10 bass. These are what I would use for stocking a pond with an EXISTING UNKNOWN fishery. IMO you have too many unknowns to stock small bass(<5"). He does have pellet trained bass in these larger sizes. This type of bass at 15-25 per 1/2 ac when fed pellets will perform well beyond average bass. These 20 bass should be a good start to 'balance out' a small existing sunfish pond to send it on a path of good kids fishing pond. If after 2 years sunfish are not getting larger and you are not seeing small 4"-6" bass you can always make more adjustments which may involve adding more 8" bass.
https://www.overtonfisheries.com/Stocker-Fish/Fish-Pricing-and-Availability Around 16-25 of these 7"-10" bass will suffice for the first stocking. You want something big enough to right away start eating small 2.5"-3" bluegill and be big enough the most average pond predator will not eat all your newly stocked bass.
IMO your 4th project before you stock any bass is to remove at least 2-3 BG/sunfish for every bass you stock. Your existing sunfish/BG will reproduce and should provide ample panfish for future angling.
At this point in time and with many unknowns I would not add any other fish until you know your existing fishery conditions. Then with more information the stocking plan can be adjusted.
Note - Overton does have larger sizes of BG and Redear Sunfish which may be a good option for you. Supplimental stocking of new larger sized fish have MUCH better survival rates when added to existing pond than small fish. IMO work with your existing fishery to wisely build on your current fish base, rather than trying to start over with a "standard" stocking plan of all small fish for a new type of pond.
