I should have just done this in the first place, but I didn't think I could get a straight answer from the IRS.

I called their help line, eventually explained my situation to an operator, who then routed me to the "Advanced Individual Situation" help center. The man I spoke to there asked me the nature of the work I am doing and said that it was clear that the income is being earned in Switzerland. He referred me to Publication 54, p. 16,
Source of Earned Income.
This section uses the example of pay for work done in Austria is income from a foreign source even if the pay is deposited directly into your account in the US and your employer is located in New York.
Yay! And thanks to those who tried to help figure this one out.