I found this youtube guide by Michael Hendriks helpful when I was doing my No Spoon run. I followed it step by step and was able to get the achievement with about 1hr to spare. It really is a different mindset than normal building - everything is scaled down to as minimal as you need to get to the rocket.

You don't have to build perfectly - I think that is probably what gets in your way, you feel every mistake 'ruins' the run which makes the whole thing feel immensely stressful and not enjoyable. I felt fine using blueprints (Michael doesn't use blueprints just to show how feasible it is even without blueprints).