Well, it's not certain that nothing can be done.
Assuming that the neck is in fact intended for that horn, it might have been cut down, or even made incorrectly. If you could temporarily extend the mouthpiece to the point that you could get a medium length note (say, 1st octave G) to play in tune, IF then you would find all the other notes are well in tune, it would tell you that the problem is a mechanical problem of the neck's length, and it can be easily fixed. On the other hand, if you do this and all the short notes are way flat and the long tube notes are somewhat sharp, it would tell you the horn was designed for a different pitch.
When doing this, I'd set a tuner at 440, then repeat the exercise with the tuner set at 442.
You can also put the mouthpiece on the neck and slide it back and forth till all the notes are in tune with each other, then determine what pitch is the A. If as I suspect you cannot find a point on the cork where all the notes are in tune with each other (irregardless of the absolute pitch standard), then it'll be that the neck's too short. On the other hand, if you find that the horn is very well in tune WITH ITSELF at a mechanically sound position on the cork, but the tuner has to be set at A = 460 or something, then you've got a real oddball.
Thing is, there are VERY FEW saxophones that truly play "out of tune". I very much doubt you've somehow ended up with one.