From a rhetorical point of view, the biomoderate singularity probably works better than the non-moderate version since it contains less outrageous and "silly" elements. It even fits with the "machines of loving grace" ideas about AI worlds that got crowded out by the superintelligent AI memes somewhere in the late 80's.

In practice I doubt people attracted to bioconservatism would go for singularity thinking, simply because they might be dominated by the ingroup, authority and purity moral foundations in Jonathan Haidt's system. If you think that there exists a natural order or a historical structure that shouldn't be overthrown, then a singularity may not be what you want.

I think a common assumption is that singularities are highly contingent affairs, where the range of potential outcomes is enormous. That makes it sensible to try to get a singularity with the right dynamics to get to the outcome set one likes. This assumption is likely based on the fact that the smarter a being is, the more behavioural and mental flexibility it exhibits, and singularities presumably involve lots of smarts. But there could be strong attractors in singularity dynamics, essentially imploding the range of outcomes (e.g. something akin to Robin's cosmic common locusts). In this case the choice might be between just a few attractors - if we even can know them beforehand.