Form 1116 is not used to report income. (I.e. to include US taxable income so that tax will be calculated based on it.)
Rather it is used to indicate what part of US taxable income reported elsewhere is from a foreign source. If foreign-sourced income is taxed by a foreign government, some of that tax may be allowed as a credit against US tax. That is the foreign tax credit (FTC) and is what the 1116 process will compute. It is limited to the the total US tax times [foreign source income by type / world-wide income]. That is the tax code 904 limitation and sometimes produces counter-intuitive results. https://www.law.cornell.edu/uscode/text/26/904
[The FTC does not give back foreign taxes. Rather it reduces US tax on the same income. Usually US tax is so low that you wind up paying significant foreign tax. But you don't also pay US tax on the same income. Usually.]
So you have to find a way to get the foreign social security income into your TT/US tax income. A "dummy" 1099-R seems like a reasonable way to do this.
But as you suggest you cannot include foreign income tax withheld on the 1099-R because it is not paid to the IRS. You do that in the FTC/1116 part of TT. Remember to convert to USD.
Also check to see if there is a tax treaty between the US and the country involved. Sometimes social security might be treated specially. https://www.irs.gov/businesses/international-businesses/united-states-income-tax-treaties-a-to-z
Also a lot can depend upon your country of resident (US vs. foreign) as the tax treaties may change the source (foreign or domestic) of income based upon residency.
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