...Hunh. I just tested out your example words, and yep, I do the same thing with the two different eees. Or, well, an equivalent that matches your description; I don't know that it's exactly the same, since my accent is middle-of-the-road newscaster American. (Midwestern American, that is to say, of the enunciated sort. I get a bit more regionalized to Ohio or New England on specific words, but that's my general accent.)