I think that is the best solution. If you can get larger LCS, say 6" plus, you can stock fingerling LMB 2"-3" fish at the same time or shortly after. The LCS should stay bigger than the LMB's mouth for some time and allow the LCS to pull off at least one if not two spawns before the LMB would get to a size where they could feed on your original stocker LCS if ever. The LMB will actively feed on the FHM keeping them under control while not being large enough to feed on your larger LCS. The FHM will also take pressure off your first couple LCS spawns, giving them a better chance of taking hold.
Have you thought about stocking grass shrimp in your pond as well? They would also be a good food source for your BG and immature LMB... Palaemonetes paludosus which is a Florida species of freshwater grass shrimp should be found rather commonly in most vegetated waters in your area which should lead to easy collecting. A few dozen stocked now should lead to a solid population in the future, particularly if you have some vegetation already present in your pond...
