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I don't know this for a fact, but sensibly one might expect iTunes and Logic to use the same mp3 encoder, since you'd hope that Apple would want their best in both.
So maybe try a completely different one, say LAME, to see if that makes any difference.
You say the EQ curve is fairly typical, have you looked at a spectral view? Stuff outside of the mp3 bandwidth shouldn't affect a properly implemented encoder, but we don't know if it's been properly implemented, try low pass filtering above 16kHz, and see if the encoder manages better.
Finally, why mp3? AAC is superior and I think you'll find it on most players these days.
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