Pilgrim, I think what we have here is a failure to communicate. This is getting a little frustrating as I'm appealing to scripture, history, systematic theology, DeCartian logic, and anything else I can come up with, and I'm frankly feeling ignored as you chant "exegete, exegete." Do we even agree of the definition of the word "exegete?" Let's just make sure. Let me quote from one of my old college textbooks, The Moody Handbook of Theology by Paul Enns: "Biblical theology has a direct relationship to exegesis (to explain; to interpret), inasmuch as biblical theology is the result of exegesis. Exegesis calls for an analysis of the biblical text according to the literal-grammatical-historical methodology." The passage should be studied in its historical context. What were the political, social, and particularly the cultural circumstances surrounding it?" In another of my favorite broad-subject references, Millard Erickson in Christian Theology, 2nd ed., explains the steps to "doing" theology, and lists steps 5 through 7 as consultation of other cultural perspectives, identification of the essence of the doctrine, and illumination from extrabiblical sources, respectively. Thus, according to how I've been taught, all that I've been giving you, Jewish history (which is not something that is iffy or in question, but something that Jews are as confident in as you are that Columbus sailed the ocean blue in 1492), occurrences of the tallit in OT and NT (though admittedly, not having it's use spelled out), and appeals to NT themes ARE EXEGETICAL! What more do you want?
If what you mean by "exegete" is that you wish to narrow the field of the burden of proof to 1 Corinthians, Chapter 11, and Chapter 11 only, then we are not operating on the same field. Taken in isolation, yours is the only view one can reach. However, taking a verse, a chapter, or even a book of the bible out of it's FULL exegetical context of the rest of scripture as well as history and culture, is not sound theology by any orthodox measure. I'm not accusing you of being less-than-orthodox, I'm just clearing up definitions, because we are really missing each other somewhere. Yell if I hit on it. :-)
As far as my commentary on the passage, just in case that's what you mean, what is left after I exegetically disprove (even if only to myself) that the specific symbols do not matter? Easy, everything is left. The scripture is rich with meaning, if we are not distracted with women's fashion! According to the order and purpose of their creation, and even as we can observe in "extrabiblical" natural revelation, men are to act like men and women are to act like women. Women should submit to the leadership and authority of men, especially in the liturgy, and they should show honor and respect to their husbands, even as their husbands show honor and respect to Christ, publicly, tastefully, proudly, and in a uniform and conformal matter. Respect and conformity are foundational in every church. No, you can't make up your own, individual ways, it has to be something widely excepted, and women wearing hats while men do not is one excellent way of doing that, but obviously not the only way. (obvious because of the larger exegetical context)
As you can tell, I focus most of my attention on the issue of the men not being permitted to have their head covered, because this is the half of the issue that we can see difference between Jews and Gentiles. One possible explanation about his appeal to the other churches at the end would be that he was specifically speaking of the women, where it was (and is) also the Jewish practice that women wear a shawl as well as the men. So on the issue of women, there would be universality. But on the issue of men, there would not be. And if there was not, then that proves that the symbol is not important (for either sex, logically).
Aside from the fact that Jesus Himself wore a tallit, I think my strongest point is something that you've hitherto ignored as well, and that is that Paul's reversal of tradition or law or at least traditional interpretation of the law, not just exempting but forbidding an age-old Hebrew practice, stands out like a sore thumb from the theological makeup of the New Testament. The only other thing I can think of that comes close is the doctrine that animal sacrifices should no longer be performed, and that was dealt with in detail and at length and logically explained that Christ was the final sacrifice. (that's a pretty big deal) Why is there no such lengthy and logical explanation for the cessation of tallit use? Moreover, Paul is famed for teaching our freedom from the law, and rebuking the Pharisees and the legalists who would impose physical laws like circumcision or kosher butchering on Christians. For Paul to now introduce this law of dress code seems to defeat everything else he ever taught about law and grace. How do you exegete that? (use any text you like, even extrabibilical as long as it's accurate, I don't mind.)
