Yeah, Clinton, the really expensive ones have sliding fipples already, so it's only on the cheap ones that you need to risk ruining the thing to make it tune.If it's pushed in as far as it will go, as you say, you may need to take the mouthpiece off and dremel the thing. Thank goodness for Dremel, eh?
You can hear when something's only a couple of cents flat? You have a better ear than I do.
Alex