Hey mate! Good going! You are doing superbly well, your first cold approach led to moving her and a long convo and a number? That's absolutely awesome, I'm totally impressed!!
You asked about willpower, well I don't think willpower plays as big a role as you're thinking. You need willpower to get yourself out of the house and set your goal (like talking to 6 women)... once you get out there it's more about (1) momentum, (2) being in the moment, and training your brain to see->approach without hesitation. I will try to explain.
Momentum... if you have a long interaction, e.g. 20 minutes I think you said, you'll lose momentum and have to regain it, this is totally normal. Treat the next few approaches as practice, likely your facial expression won't be on point or you'll be nervous or anxious, but after one or two approaches this goes away. When you're fully relaxed and warmed up, witty banter, etc, flows naturally and self-doubt vanishes.
Being in the moment... this means not overthinking shit, like hesitating or rehearsing your approach... and training your brain, see
this article, it will change the way you think about approaching. Of course, continue the newbie assignment, because it gradually acclimatizes you to the concepts, but as approaching becomes more normal to you, do follow the tips in the article. They work great for me. They have another tip which I do not always follow, but have tried in the past as an exercise: When you see a hot woman,
run up to her... don't think, just run. This removes the possibility for hesitation and also shows her that you're 100% in the moment and not shy to go after what you want.
Again,
great approaching, let me know if you need any other help or advice. Stick at it my brother
Ray