This is my first post!

So yes, I did find this forum by searching "Fantasie Impromptu" on Google and reading the breadboy thread. And I did search up FI like you guys say to do in all the other FI threads. So I hope that people aren't annoyed with yet another FI thread, and that I haven't made an embarrassing oversight, my question already answered elsewhere.
I just started learning FI (I hope not for the wrong reasons), and the polyrhythm thing is just about killing me. Most of the internet suggestions I've read fall into one of the following two categories:
1) Hands Together:
First work out the 4 on 3 sequence in twelfths. Practice tapping the rhythm, tapping 3 times with your left hand for every 4 taps of the right hand. Then start slowly on the piano. Use a metronome if necessary. Get faster and faster slowly, until you reach the desired speed. This process is necessary so that you play accurately.
2) Hands Independently:
Practice each hand separately until you can play each part very fluently. Then just play them at the same time!
This is all nice,... except for the fact that the two are BLATANT CONTRADICTIONS

I am very afraid of learning the entire piece too quickly, realizing it is super-sloppy, and not being able to correct bad habits. This suggests I follow (1). At the same time I can hardly imagine "feeling" the twelfth rhythm at high speeds. Besides this is hardly how the music is structured. And plus it seems very difficult to speed up. Even when I try to just go up a few bpm it just degenerates into... Someone please clear this up.
Much of the advice also says that after a bit it will just "click," and you will magically be able to play it. I can slowly play some of the measures with both hands, but it's nothing like a magical feeling of accomplishment. It's more like balancing a stick on the end of your nose... I feel like it's all going to come apart any millisecond, and I'm not even sure if I have it right---the moment I try to listen to one hand to see if it's even, the other hand forgets what it's supposed to do.
Am I panicking too early?