Can Sola Gratia Survive Without Sola Fide?

Paul's argument in Romans 4 is especially germane to our discussion of the doctrine of Sola Fide in general, and of the relationship of faith to works in particular. Some relevant points include:

1. "Works" and "faith" are set in antithesis to one another: "Now to the one who works, his wages are not counted as a gift but as his due. And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness" (vv. 4-5).

2. The works that Abraham is said not to have done cannot be understood to be "works of the law," for Paul says explicitly that "the promise... did not come through the law but through the righteousness of faith" (v. 13). Plus, Abraham predated Moses by 430 years (cf. Gal. 3:17), meaning that Mosaic "Jewish boundary markers" could not have been in view (vv. 9-12).

3. Paul hints here at what he says explicitly elsewhere: there are two kinds of righteousness, one based on the law, and another based on faith (cf. Phil. 3:9).

4. The word logizomai ("reckon, count, impute") is used 11 times in this chapter.

5. Lastly and perhaps most importantly, according to v. 16 the fact that Abraham's justification was by faith and not works is what ensures the graciousness of the gospel: "That is why it depends on faith, in order that the promise may rest on grace and be guaranteed to all his offspring...." Please do not miss this point. The gospel is only "by grace" because it is "by faith" and not "by works."

My question for our Catholic readers is this: In the light of Romans 4, how can you affirm Sola Gratia while simultaneously denying Sola Fide?