Question to flutemakers: changing a flute's A4 standard?

I have an old Schwedler flute made likely before WW2 (it has a Bakelite raised lip plate and has a reform-embouchure). I have little to go on for identification (the best I have is that there is a “P” etched under the foot’s C# key). There was likely a stamp on the flute as I can see disturbance of the grain, but I cannot make out the maker’s name.

Through the efforts of an instrument-maker, I have managed to learn that it’s A4 standard is 437H. Tuning software fails me even then, the notes never quite hitting the middle. My teacher (a private tutor) says my notes are OK though. However to play with a regular piano I have to rotate the lip plate away from me. This raises the overall pitch enough to roughly match. But it cripples the flute’s sound and is quite uncomfortable.

Here’s my question: if I were to have a new head made for the flute, would it be possible to change it’s A4 standard from 437 to 442? Or would it not work due to the overall tuning of the flute?
Note, that the head is nickel-brass metal in its entirety.

Your flute was almost certainly built for A=435Hz (“diapason normal”) with a little sharpening capacity, hence you can just about get it up to 437 with the head pushed right in and with the embouchure excessively rolled out/open. A shorter head will not produce well-centred intonation throughout the scale at 440, let alone higher. The scaling is and will remain too long. It really isn’t possible properly to bring a Low Pitch flute up to modern Concert Pitch - even shortening the joints at the tenons and re-tuning (re-sizing) the tone-holes will not fully achieve a proper re-tuning, besides which such operations would ruin the flute. Better to accept it for what it is.

I was afraid this would be the case. My teacher guessed as such but I wanted to hear a flutemaker’s thoughts on the matter as well.

Thanks for your answer.

EDIT: Can I ask another question? My flute’s stopper has a cork that has the flute-looking part damaged. When I use a tuner set to A4=435 I get right on the mark for most notes above G4 but get wildly fluctuating notes downward from that. May that be because of the stopper-cork?

You should also consider that tuning on flutes depends partly on how you blow it, and you should allow some range of tuning when you check the pitch of each note with a software. These type of flutes are also tuned not in equal temperament like a piano.

I think a retuning with some major work could be done. German flutes have small holes, so a combination of hole enlarging, joint shortening and perhaps (but not necessarily) reboring should work. Of course the resulting sound will be very different from what it has now.