Can't e-file form 1040 without W-2, but cannot get W-2 due to working in foreign country. How can I file?

How can I e-file my taxes if my employer is not an American company (no Employer ID Number) and will not provide me with a W-2?

I already reported my foreign earned income with form 2555 but this apparently cannot be filed on its own. I just keep getting the same "you're not eligible for e-filing" message and I don't understand how I can complete my tax return without a 1040.

Is there any way I can file/add information to a form 1040 without a W-2?