Keep taking LMB out... If you aren't seeing much in increased growth rates, you still have too many.
Adult BG are your best bet for continued presence in your pond. 6"+ fish would be best. Fewer BG of that sized as compared to more in the smaller size range would be better if money constraints are an issue.
As to whether GSH will last and continue to reproduce in your pond... There are several factors. First off, does your pond have an over abundance of LMB? From the sounds of it, yes. That is going to be the biggest factor and challenge is getting GSH to permanently establish in your pond. Does your pond have cover? Particularly vegetation? Some vegetation is a good thing, roughly 20% of you pond... Are the banks of your pond extremely steep with minimal shallow areas? If your pond is lacking shallow areas, it is lacking brooding areas for YOY GSH. Source the largest GSH you can find and stock them in mid to late April. If conditions are right, they should spawn shortly after stocking and give you the best chance at them taking hold. You can also just stock large numbers of GSH each year realizing they'll just be expensive snacks if you don't have the right habitat. It's just pricey doing that.
Are there other species present in the pond besides BG and LMB, like crappies or catfish?