There seem to be a couple of confusions here. First, evolution is not a global optimization algorithm; all species are in the vicinity of local optima, not some global optimum (if that even means anything biologically). Second, while evolution is stochastic, it is strictly a local search procedure, at least in metazoans. Evolution will explore slightly suboptimal solutions, but strongly suboptimal ones will never last long enough for a species to move through that trough, and lethal solutions are impassible. Are there workable paths between the regions of viability? That question can only be answered empirically at this point, not by the kind of abstract argument you're using here.
Larger jumps (large insertions and deletions, for example) are possible, but as their effect gets larger, the probability of their hitting a viable solution drops sharply. This is true not only because the great majority of genome space is not viable (so picking random points is a very bad strategy), but also because offspring inherit not only a (possibly modified) genome from their parents, but also a developmental environment (e.g. the chemical environment of a fertilized egg). That environment is unlikely to support development of a very different organism.