Let's say some event caused runaway glacial melt, and removed half of the ice currently locked away in specific areas of the planet. Would the significant weight changes on various plates and fault lines be enough to dramatically shift how current plates were biased against one another?
Yes, it's called glacial rebound. Some areas of the globe are still responding to the disappearance of the ice of the last ice age. A well known example of this are the raised beaches in the northern Baltic, where the crust is rising due the melting of the ice sheet that covered Scandinavia.