I feel your pain. The Chilean income tax system is so easy to use.
I am in no way a U.S. tax expert ( very far from it); however, I do not believe your employer needs a tax payer id number for you to file a 2555. You should not need a w-2 form from your employer, and I don't remember ever seeing anything requesting one on the form. You likely want to hang on to any contracts you might have that layout your employment terms and payment stubs and such, but that should do the trick as far as evidence is concerned.
For example, I am employed by a Chilean company I own and I am not required to issue a W-2 to myself as far as I know as an employee of that company because it is not an American company subject to U.S. jurisdiction to claim my income exclusion on form 2555. They do ask for name and address, plus some other stuff regarding your employer on the form.
I think it is H&R block that has online efile that can handle the foreign payments. You can fill out there form, and test everything, and you do not pay until the last steps when you are happy with everything.
Personally I prefer to do everything with a very cryptic quill and ink to encourage lazy auditors to leave me alone.
