I've decided to post as an answer (revised versions of) my comments and include some additional suggestions, because at this point none of the answers seem to specifically address the teaching of logic to high school students.
The first 2 (first 3?) Project MEGSSS Elements of Mathematics books cover propositional logic, predicate logic, and set theory, and they were written for strong high school students. I own several of these books (including the logic books), but I'm not especially impressed with them (see my 5 September 1999 comments in the Math Forum group math-teach). Nonetheless, since they were specifically written for high ability high school students, I recommend that you investigate the possibility of examining these books.
When I first saw a few of the Elements of Mathematics books in March 1988 (I was a substitute teacher for a teacher who used the books for a special city-wide honors program), what I did at that time was to write a snail-mail letter to the organization. After perhaps two weeks, I received a price list from them, and using the price list I ordered a few of the books. I don't know what to suggest now, however. The information on their web pages seems strangely opaque about how to purchase their books (without formally signing up for the full-fledged program), and amazon.com seems thus far to have overlooked the existence of these books.
As someone who has taught in a high school of the type you describe (during the 1990s), I think it would be well worth your while to spend a day, if possible when you're not teaching, looking through books in a large University library. You know best what will work for you, and this is the quickest way I know of to carefully examine dozens (maybe over 100) logic textbooks. In U.S. university libraries, most of the logic texts will have Library of Congress catalog numbers that begin with BC 135 or begin with QA 9. If the university library has department branches, you will want to look (for BC 135 and QA 9 books) in the mathematics library, in the philosophy library, and in the general campus library.
Herman Rubin has often posted (in sci.math, mainly in the 1990s and early 2000s) about children learning logic, so you might want to search for things he has written. You can also find his comments in other places as well, such as p. 9 of the January 2008 thread teaching algebra to elementary school students in ParentingBanter.com under the category "misc.kids-General". The Suppes and Hill logic book that Rubin refers to in these 2008 posts is
First Course in Mathematical Logic by Patrick Suppes and Shirley Hill (1964; reprinted by Dover Publications in 2002)
and the book by his wife (she died in 2002) that Rubin also mentions is
Mathematical Logic: Application and Theory by Jean E. Rubin (1990).
According to the Preface of the Suppes/Hill book, an earlier version of their book was used in 10 high school classes in an experimental program co-sponsored by the U.S. National Science Foundation and the U.S. Department of Education.
Patrick Suppes appears to have done a fair amount of research into children learning logic, as the google search Suppes logic children will show. Specifically, you may want to look at the following:
Mathematical logic for the schools by Patric Suppes (1962)
Young children's comprehension of logical connectives by Patrick Suppes and Shirley Feldman (1969)
