I doubt either will control the BG population overly well. It'll take a few years for even BC to get large enough to effectively prey on 3"-4" CNBG.
You could consider adding some HSB, they aren't the best at controlling BG but would help. They also take to pellets well and are excellent for angling and many find them good on the table. They rarely if ever reproduce in ponds, so they are not a management issue.
You could also add just 1 LMB. Just that one bass can help... Or if you can, try to source all male or all female bass. Add a dozen or so in the 12-14" range. Spring is often easiest for IDing male bass as you can squeeze them and check for milt as you catch them off their nests.
