Overcorrection resulting in Oscillation is a real problem in the process industry. Oil refineries, dairies, paper plants, etc. My dad worked in this industry for 50 years and was one of the pioneers in how these facilities are controlled and laid out. Process control uses a
PID to keep things from getting out of hand.
But in your situation, what I would do is when you are going to have a
reaction, multiply by .8 before applying it. This way you will never overreact. Instead, you'll see a target and creep up on it, rather than the chance of overshooting it.