That's a very good analysis and I agree with your conclusions. It still leaves one lingering question, though. According to the movie, the supernova happened before Spock could get there, but he still deployed the Red Matter anyway. Why? The star had already emitted its radiation and blown off its atmosphere. The damage had already been done. There was no way the black hole could magically suck all that radiation back in, any more than handcuffing someone after they clap their hands could keep people from hearing the sound of the clap. And Romulus and Remus were already gone. So why go through with a plan that had already been rendered irrelevant? What good did it do at that point to deploy the Red Matter? This is the one part of the movie's supernova scenario that
Picard hasn't found a more plausible explanation for.
The simplest explanation I can think of: After a Type II supernova happens, the expanding shell of superheated stellar atmosphere continues releasing radiation for months. At first, that radiation is largely contained because the ionized hydrogen around it is opaque to it, but as the cloud expands and cools, the hydrogen becomes transparent and the radiation escapes. So maybe Spock was trying to reduce the amount of radiation that would be released at that time. Maybe, instead of shooting the red matter into the core of the already-exploded star, he shot it on a trajectory that would orbit the core, sweeping through the hydrogen shell and sucking up as much of it as possible before its radiation was released. So it was a last-ditch attempt to at least moderate the amount of radiation the supernova would release in the long term.
A more remote possibility is that it was some variant of a
pulsation pair-instability supernova, a rare type where the star actually survives the first eruption and then goes through another later on. This should only happen to really, really gigantic stars, but it's anomalous enough for a star with an inhabited planet to go supernova at all, so maybe there was something abnormal about this supernova.