How to report Foreign Earned Self-Employment Income?

I live and work abroad as a contractor. I'm looking for the right way to declare my (foreign earned) self-employment income, in such a way that I will end up paying Self-Employment Tax, and also be able to claim the Foreign Earned Income Exclusion (reducing Income Tax).

• Entering my earnings in the "Self-Employment Income" section only is what I would do if I lived in the US. Note that I do not have any 1099 and I pick the "cash payments" flow.
  This results in paying both Self-Employment Tax & Income Tax. I cannot find a way to later characterize this income as "foreign earned" so as to claim the FEIC (while still pay the SE tax!)
• Entering my earnings in the "Foreign Earned Income" section only does not result in paying the Self-Employment Tax. 
  This isn't the desired outcome either, even if this flow allows claiming the FEIC.
• Entering my earnings in both sections ends up double counting my income (I verified by inspecting the 1040 preview).

It feels like I should be able to enter my earnings in the Self-Employment Income section, which is what triggers paying the SE tax (good), and then be able to say this income was foreign, so I can later claim the FEIC. However, the "foreign" concept only seems to exist in the "Foreign Earned Income" section, which itself doesn't have any concept of Self-Employment type of income.

This scenario is what the IRS describes here (emphasis mine):

Self-employment income: A qualifying individual may claim the foreign earned income exclusion on foreign earned self-employment income. The excluded amount will reduce your regular income tax but will not reduce your self-employment tax.