I think your understanding of how the tax is calculated is correct. The calculation is done according to the tax law, not according to your wishes or expectations.
It's not double taxation. You are not paying any tax on the excluded foreign income. But the foreign income is not completely ignored. Your other income, that is not excluded, is taxed at the same rates that would have applied to that income if you did not get the exclusion. The non-excluded income is "stacked" on top of the excluded income for the purpose of calculating the tax on the non-excluded income. Therefore the excluded foreign income pushes some of your other, non-excluded income into a higher tax bracket. So the added tax is additional tax on your non-excluded income, not tax on the foreign earned income.
There is no way to have your tax calculated as if you didn't have the foreign income. This is the way the foreign earned income exclusion works.
