Strictly speaking, one can't falsify with any method outside of deductive logic -- even your own Severity Principle only claims to warrant hypotheses, not falsify their negations. Bayesian statistical analysis is just the same in this regard.

A Bayesian analysis doesn't need to start with an exhaustive set of hypotheses to justify discarding some of them. Suppose we have a set of mutually exclusive but not exhaustive hypotheses. The posterior probability of an hypothesis under the assumption that the set is exhaustive is an upper bound for its posterior probability in an analysis with an expanded set of hypotheses. A more complete set can only make a hypotheses less likely, so if its posterior probability is already so low that it would have a negligible effect on subsequent calculations, it can safely be discarded.

But in fact they want interesting, informative, risky theories and genuine explanations. This goes against the Bayesian probabilist ideal.

I'm a Bayesian probabilist, and it doesn't go against my ideal. I think you're attacking philosophical subjective Bayesianism, but I don't think that's the kind of Bayesianism to which lukeprog is referring.