The second spring on that is just a return spring for the remote control, it does not affect the governor. It just biases the speed setting lever to make it easier to adjust via a very inefficient Bowden cable, it does not affect the butterfly throttle's position. You can see a similar deal, where a monstrous additional spring was used for that purpose, on Kirby Lauson (Tecumseh) mower engines of about that period. I don't care for the mechanism - the genuine B&S one I posted seems much more elegant to me - and yours had a kinked Bowden cable right at the anchor point as well, but it has no bearing on your governor instability. So what did you do to fix the instability: tune the mixture?