As noted earlier, the Superhappies don't appear to be concerned about the presumed ability of the Babyeaters to make supernovas. Perhaps they have a way of countering the effect, and have already injected anti-supernova magicons through the starline network back to Earth and Babyeater Prime. In that case trying to detonate either immediately or at Huygens would fail, while eliminating any trust the Superhappies had in us. Maybe that's not much worse; they wouldn't punish us for the attempt, it might just make them more aggressive about fixing us.

Also, is the cosmology such that the general lack of visible supernovas is significant? It would seem that the normal development for "human-like" technological civilizations is that shortly after discovering the Alderson drive, a mad scientist or misguided experiment blows up the home star. Babyeaters and Superhappies apparently avoided this by having some form of a singleton, and humans got lucky because the scientists were able to suppress the information. Humans may be the most individualistic technological civilization in the universe.