I just scanned the thread, so please excuse me if I am incorrect, at the very least, perhaps I will be of help anyways.
What you are referring to could be an overtone. Take a second and whistle a few notes going up and down. What happens in your mouth when you do this? Your tongue should be going up and down slightly.
Now...time to apply this discovery to the saxophone. Just using the mouthpiece, blow as loudly as you can. Get a piano and figure out what pitch is coming out of the sax.
Work with the mouthpiece every day, and try getting different pitches on it, playing a scale of sorts. To do this, use the same tongue motions you do when you whistle. It may take a while, but eventually you'll get it.
Now, overtones. Finger low C, and try, while keeping the low C keys pressed, to play a higher pitch. Do not adjust your embouchure for this! Just use your tongue going up and down. With work, high C will pop out. Play exercises with every low note on this. Play the low note, then while keeping the fingering jump to the high note, then push the fingers for the high note, then switch fingers to the low note but play the higher pitch, then drop down to the lower pitch. This is slightly confusing, but if you write out what I just described on a music staff it will make more sense.
With practice on overtones and the mouthpiece, you will gain much greater control of the air. When your tongue goes up, the air in your mouth goes faster, which is useful for high notes. Always keep your embouchure fairly loose, and don't tighten up for high notes, or low notes. Keep it open and loose, use lots of air, and CONTROL.
Synopsis:
With all of this, unless it's a mechanical difficulty with the sax itself, I am thinking that possibly this is an embouchure issue. You're probably just too tight for tenor, which requires you to have a much looser embouchure than alto. Nevertheless, the activities I mentioned above are very useful to gain better control and sound on all saxophones.
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