You would not merely show up to court with screenshots . . . Emails can be verified by service providers.
This is absolutely a valid concern. You are not likely to get far by running away with a stolen manuscript, but concepts can absolutely be written into another manuscript. I understand the stance that ideas are worthless without good execution, but I do not believe that is a fair blanket statement. For example, good mystery plots can be agonizing to piece together. This might be controversial, but I would feel more comfortable sending high-concept fiction to editors/betas who are not active writers. Some editors/beta site their writing accomplishments as reasons to send them your work, but I'm not writing novels to the writing community. I'm writing for the general public.
You seem to be laboring under a woeful misunderstanding of how copyright actually functions, and how case actually work.
Concepts are in and of themselves not copywriteable. Neither are plots. It is the specific expression, the actual words of the text, not the elements of the plot, that are protected.
If you are in fact concerned about protecting your copyright there are two things that you would need to prove, at a minimum.
1. That you are responsible for the creation of the work. This involves not only evidence (drafts with your notes and hand writing, a series of dated drafts, notes and research) but supporting evidence in the form of correspondence with editors, beta readers, etc. This is tied to asserting your copyright. If you are going to sue, register the work before you do. There's a time limit, and the penalties are greater if you win for a work you have registered.
2. That your unique expression has been illicitly used. This means proving the similarities in the expression (the words and sentences) rather than just the plot. This is actually the hardest part in terms of convincing the jury.
3. An unpublished work by an unknown isn't generally worth much; you need to prove that you have financially suffered.
IANAL. This is not legal advice. I've just been at and involved in a fair number of copyright cases as an expert witness.