> I find it difficult to use logic when a) you don't really know all the premises that you're starting from and b) you have a material / emotional / ideological / or identity-driven stake in the outcome.

Does it being difficult mean that other approaches are better? Point b is basically saying you have a vested interest (emotionally) in it (the topic, whatever it may be) being a certain way. Foregoing rationality and logic in favour of something else isn’t going to get you better results. Most often, it means you will instead argue based on feelings and emotion. Better would be to find a way to take a step back and re-evaluate your stance.

As for point a, the only solution I can see to that is to seek more information.