The one thing in there I haven't really comprehended is thu-zero exponential FM. Seems like exponential curves are asymptotic to zero. How you going through the zero frequency then?
I see @RobertSyrett's point. A traditional exponential curve y=a^x never goes negative for any value of x. As Robert says it is asymptotic to zero. You could certainly offset the curve from the origin, but I'm not sure I see the point. As I understand it, through-zero behavior is mostly of interest with respect to FM synthesis where a linear response would typically be more useful. Another area where it could be of interest would be LFO modulation, but again it would seem that a linear response would make more sense.