What Works Are Excluded from Justification?

I have had discussions with both Mormons and Catholics about Romans 3:28: "For we hold that one is justified by faith apart from the works of the law." The topic was the doctrine of both groups that a person is justified by a mixture of faith and works, instead of by faith alone. They denied that a person is justified by faith alone, claiming that Paul rejects the works of the Mosaic code, such as circumcision, as contributing to justification. That is, they restrict the meaning of "law" just to the rules and ceremonies given to Israel through Moses. 

What neither will mention is Paul's other uses of "law," especially in Galatians. In Galatians 4:21-26, 28-31, he makes a case: "Tell me, you who desire to be under the law, do you not listen to the law? For it is written that Abraham had two sons, one by a slave woman and one by a free woman. But the son of the slave was born according to the flesh, while the son of the free woman was born through promise. Now this may be interpreted allegorically: these women are two covenants. One is from Mount Sinai, bearing children for slavery; she is Hagar. Now Hagar is Mount Sinai in Arabia, she corresponds to the present Jerusalem for she is in slavery with her children. But the Jerusalem above is free, and she is our mother... Now you, brothers, like Isaac, are children of promise. But, just as at that time he who was born according to the flesh persecuted him who was born according to the Spirit, so also it is now. But what does the Scripture say? 'Cast out the slave woman and her son, for the son of the slave woman shall not inherit with the son of the free woman.' So, brothers, we are not children of the slave but of the free woman." 

Paul makes a very clear distinction here. Is it between works of the Mosaic law and other works? Clearly not. Anyone with a modicum of biblical knowledge knows that Abraham lived four-hundred years before  Moses. Rather, he uses "law" to describe the works of the flesh, such as those of Moses, using the label of the part to represent the whole (a synecdoche), in distinction from the promise, which he uses to label grace alone through faith alone.