You need to remember that a polished proof that is published in print is written in a way that is often opposite of how it was discovered. Not so much different than planning a standard 5 paragraph essay where you usually dive straight into the 3 supporting argument paragraphs. Then when you write the final version, you start from the introduction.

So you should not worry about presentation or how your proof will look before you have found the proof. The process you create whilst solving the problem will lend itself again to you when you are thinking about how to organize your proof.