Are the offspring of your HBG reverting to a GSF body habitus? Mine did, after 8 years I have fish that are morphologically indistinguishable [by a presbyopic novice like me] from native GSF, and follow GSF behaviors. In this setting, with a more slender, less prolific forage, you might well be able to manage the HBG and their offspring with an initial stocking of multiple adult SMB. You might need to manually remove HBG/F2s larger than the SMB could handle, but I would guess after a couple years and a couple SMB good spawns, and with further regression to the GSF phenotype, you'd have good control.
The SMB won't be able to control native BG, so if you have a mix of native BG and HBG, you'll likely need to go another route.
I completely agree with Bill's comments about water temperature and quality.
