Re: pitch problems on old bari sax
I think it would be best if you were more specific. When an instrument plays "Sharp" the logical answer is to pull the mouthpiece out. When that is no longer possible (because there is no more neck to hold the mouthpiece) then an extension may need to be built.
If pulling the mouthpiece out makes the whole horn out of whack, it will do good to find out what exactly is thrown off by pulling the mouthpiece out further. I play a vintage instrument with a modern mouthpiece. If I put the mouthpiece on where it might seem to go, the horn plays sharp. I had to build an extension on Mouthpiece to hold in further out from the horn. Now, it plays in tune.
If you lower the heights of the keys to correct general intonation, rather than targeting a specific area, you will likely end up with extremely sharp palm keys notes. The bell key notes are also going to be very sharp. You will also likely end up with a stuffy horn.
It sounds to me like the problem is the mouthpiece/horn combination the band director is using. If she loves the way the mouthpiece sounds on that horn you may need to modify something to get it to work. If not, try a larger chamber mouthpiece. Mouthpieces that will play well on a Buescher Bari include: A Babbitt, Old Brihardts, Caravan, Rascher, vintage links (large chamber), Vintage Woodinds, vintage Buescher, vintage Conn, vintage Martin I'm sure there are many others.
Best of luck!