The changepoint detector's --dispersion option scales its penalty by how over-dispersed the squared residuals are. That factor is measured on a fit that already contains the false breaks, so we tried re-measuring it on the refit and fitting again.
On 200 seeded null series of 200 points, false alarms went from 30% to 27% on GARCH noise, 29% to 22% on t3 noise and stayed near 40% on AR(1). Detection of a real variance break moved by 4 points at most. Two extra rounds buy almost nothing, because what is left is the noise's memory, which a scale factor cannot remove. The single pass stays the default and a GARCH likelihood cost is the next route.
Script and output: ventures/changepoint-detector/eval/meanvar-dispersion-iter.mjs.