Hi Andy --
What tone exercises are you using, or how are you currently working to solve this problem?
I would suggest, if you haven't used it already, the Moyse collection "De la Sonorite". It's published by Alphonse Leduc (which means overpriced
. But it has some terrific exercises in it that can and will develop your tone.
I, too, started with great difficulty in the lower register; most likely because I began playing on a student level Gemeinhardt. However, since you've had others play your flute and it seems not to be a mechanical problem, there is work for you to do on your embouchure to develop it more.
If you cannot afford De la Sonorite, I would suggest two wonderful exercises from it that, after 30 years of playing, I still use as my normal warm up:
1. Begin on top line F. At 60=quarter note (and use a metronome here), play quarter notes F, F#,F, G, F G# . . . and that pattern all the way up to high C. Then do the same thing going all the way down to low C (or B): top line F, E, F, Eb, F, D . . . all the way down. The first time you do these exercises, play all of the notes short, but solid and not cracked. The second time, slur two notes at a time: F-F#, F-G (slurred) and so on. Your next pattern will start from the note above and slurred: F#-F, G-F, and so on.
After you've done all of this going up and down the scale from F, then play the sequence in triplets up and triplets down: F, F#, F would be your first triplet to each quarter note (at 60).
While you do this mammoth exercise pay particular attention to the quality of sound you are getting from every single note. Make sure every single one is clear, not cracked, and solid. When you begin the slurring exercises, make sure it is even and no break between notes -- as smooth as possible (yes, it gets much more difficult to do that as the interval between notes increases; that's why it's an exercise
)
2. Begin on B just above the staff and use the rhythmic pattern of quarter note followed by dotted half, and at 60=quarter note. Go from B down to Bb, B-A, B-Ab . . . all the way down to low C or B.
Once you do that, then do the same pattern up to high C (B-C, B-C# . . .)
It's extremely important in both exercises to NOT rush them and to discipline yourself not to be satisfied with a cracked note. This is not a technical exercise; it is a tone exercise. If you crack a note, repeat it if you like. The more important concern is not to get all the notes right, it is to get the best sound you can on all those notes.
Try those out and see how you do. Good luck!
SK
She is a very aggressive player, and slightly intimidating, but all around excellent.