In one of the comments, Professor Lawrence Kaplan makes reference to J. David Bleich writing on this issue. After a quick google search, I found that Rabbi Bleich had written on the issue in Tradition magazine in 1980 (I assume that this is the essay Prof. Kaplan was referencing).
In reading through the article (I have included quotes below), it seems that at least instruction on the seven Noahide laws should not be a problem or concern. What is interesting is that one of the things that I have learned from Rabbi Shlomo Singer's shiurim is that you can't divide up the Talmud. He is fond of saying, it is "one page" -- all sections, all issues are interconnected. While I haven't heard Rabbi Rosensweig say this, certainly in how he moves throughout the entire Talmud in nearly every shiur, he seems to make the same case.
With all this in mind, I must admit I feel justified in continuing my exploration and study, particularly since I do feel it helps me look at everyday life with new eyes, while at the same time helping me come closer to God, by coming closer to the Torah.
Below are some quotes from the opening and closing pages of J. David Bleich's, "Survey of Recent Halakhic Periodical Literature: Teaching Torah to Non-Jews" (Tradition, 18 (2), Summar 1980.
The prohibition against teaching Torah to non-Jews is well known to students of Jewish law. Equally well known is the role of Abraham as the "father of the multitude of nations," entrusted with the sacred task of carrying the teaching of monotheism to idolatrous peoples. A person unfamiliar with the extensive rabbinical literature devoted to this topic may perceive a certain tension, and perhaps even contradiction, between a recognized need to disseminate religious truths and an almost xenophobic reluctance to share the greatest repository of such truth—the Torah. Yet even a cursory examination of the relevant sources dispels the notion that while the community of Israel jealously guards its spiritual wealth, it refuses to share these riches with others. On the contrary, it is unique among Western religions in its willingness to share its teachings without seeking to impose its observations. This necessarily involves a vocation of teaching despite the stricture against teaching Torah to non-Jews. The latter, while based on substantive philosophical considerations and of definite halachic import, admits of sufficiently broad exclusions to assure that Israel remains true to its role as a lamp unto the nations. p192
In the medieval period no less a personage than Rambam entirely Christianity from this prohibition, while in the last century Rabbi Israel Salanter, the acclaimed founder of the Mussar movement, actually mounted a campaign for the incorporation of talmudic studies in the curricula of European schools and universities. p193
It seems to this writer that, while there exists no obligation to volunteer information (although it may well be laudable to do so), there is an obligation to respond to a request for information. Jews are commanded to disseminate Torah as widely as possible among their fellow Jews, but there is no obligation to seize the initiative in teaching the seven commandments to Noachides. Nevertheless, when information or advice is solicited there is a definite obligation to respond. When the non-Jew take the initiative in posing a query, the Jew must respond to the best of his ability. p203
Despite the absence of a specific obligation to influence non-Jews to abide by the provisions of the Noachide Code, the attempt to do so is entirely legitimate. Apart from our universal concern, fear lest “the world becomes corrupt,” as Rambam puts it, is also very much a matter of Jewish concern and self-interest. Disintegration of the moral fabric of society affects everyone. Particularly in our age we can not insulate ourselves against the pervasive cultural forces that mold human conduct. Jews have every interest in promoting a positive moral climate.
Accordingly, Jews should certainly not hesitate to make the teachings of Judaism as they bear on contemporary mores more readily accessible to fellow citizens. That is the most direct means available to us for exercising a positive influence in improving the more atmosphere in which we all live. p203