Tom and AJ,
Here's what I did to help tame it. Not perfect, far from it, but it helped. I agree with your assessment of way over the top for the breathieness of it.
Anyway:
Program>choose jazz flute>menu>effects>then play with both of the effects, changing types and lowering the send levels which is way too high on both.
The first FX "revsmthhall" give it way too much air which compounds the breath and the send level at 75 is way high. If you pick a different reverb here, it really drops the echoishness of the sound or no reverb really flattens it and you could add reverb back in the final mix.
The second fx L/C/Rdelay (left center right) then adds even more by bouncing the sound around and doubling up on it.
Terry