Chiming in a bit late…
Breath control resolution is somewhat of a tricky subject. It's very easy to assume that a 7-bit MIDI signal isn't enough, but often I've found the problem lies in the perceptual mismatch between the breath signal produced by the performer and the perceived sound intensity of a sound produced by a synth.
Because we're very sensitive to that "jitter" between "no sound" and "a very faint sound", the synth should ideally increase volume/intensity veeeery gradually in the very low range (when the CC is 0, 1, 2, etc.), even if the curve can be steeper after that.
Having more extreme curves on the Sylphyo side would be a good idea (even regardless of this particular issue), but I don't think it would really help mask the perceived discontinuity in the very low range in most cases: if the sound is too loud at CC value 1 compared to CC value 0 (silence), then it's not good.
A 14-bit signal would help a little in this case, but I'm not sure it would be practical anyway because you would need a tremendous amount of accuracy to produce a smooth signal using the breath. And it could also bring in the timing issues Laurent talked about.
The synth will be smoothing your breath signal regardless of its resolution, and it'll do it at least over 32 bits, so it'll create the intermediate values your 7-bit or 14-bit signal lacks. The real question is how the synth smooths the signal: is it a good tradeoff between no perceived discontinuities and reactivity?
To me, the solution indeed lies in the volume curve, as Clint proposed. We're very sensitive to the difference between CC values 0 and 1, but I've yet to come across people complaining that there isn't enough steps between CC values 80 and 81. Bending the synth's volume/brightness curves to our perceptual expectations is more likely to bring about the desired results, in my opinion.
Have you found a good solution for this?
If not, you could try using some kind of program (like Max from Cycling 74) to produce the MIDI data needed to play the synth at a desired breath CC level, and check whether you hear a large discontinuity between 0 and 1.
If you do, then there should be some curve bending work to do on the synth side. If not, then we could try adding some new, more extreme curves on the Sylphyo side and see if it solves the issue.