Jason - I'm home playing hooky from work so I can finish writing the conclusion on my dissertation -- does that qualify me?

And my significant other teaches history at the local university, so that's something anyway!
I don't have my copy of Writer's Market handy, but I seem to recall that CWTI requests authors to submit their references separately from the article. You might visit the magazine's website and look for their guidelines for submissions to check this. CWTI walks the fine line in presenting history -- if you footnote everything and include sources, you become a scholarly journal like the William & Mary Quarterly and then lose your mainstream market. Which is where the money is. By staying mainstream, you have to present your material in a user-friendly manner, which isn't always the most scholarly way to present.
Having myself written articles for various publications where I used direct quotes but was not required to give sources, I know that this is a standard procedure and an acceptable ones for some publications. Even when not requested, I always provide a footnoted copy along with the "popular culture" version of whatever it is just to back myself up.
Using these quotes as source material, however, is another story. Your best bet, if you can't find where the original came out of, is to do something like: "In his article in CWTI, historian John Smith relates that in a meeting after the war, Forrest told Sherman that........" And then cite John Smith, Article Title, Civil War Times Illustrated in the footnote.
The other thing you might do, if you really, really need to find the source, is to contact the magazine. You could try contacting the author as well, although a word of caution here: as you may or may not have discovered, historians, like everyone else, can be terribly jealous folks and will carefully guard sources rather than spreading the wealth around. (i.e., If you ever look into Mexican history, you will find most of the sources in Spanish which eliminates a certain portion of the population from ever finding out what is contained in them.) Asking a historian for a source can be a touchy subject.
As to using CWTI as a source, I don't see any harm as long as you are using other sources. Don't rely entirely on CWTI. Generally, you are going to need to cite 3-5 sources per page and professors like to see a nice mix of primary and secondary sources, with secondary sources including books, articles, speeches, etc.
Parenthetic to this, wait until you start using Internet sources. We are finding that most academic-types detest seeing Internet sources and some even direct students to not use any at all. There seems to be some thought that if it is printed on paper, you can accept it as fact but if it is off the Internet, it is fabricated. Personally, I would have been lost without them having found some spectacular primary source documents for my paper that I otherwise would not have know about. If you get to citing Internet sources, I have the MLA style guidelines for footnoting -- they can be tricky!
Hope this is of some help! Better get back to my paper....
Kat