Ben Levi, in case you haven’t been following the thread, the issue here is not what the woman should do, and not what beis din should do. It’s what the husband should do.
I may agree with you regarding his right to use the get as leverage to be given what is rightfully his (and Sam will likely still disagree), but Lior said nothing about custody arrangements in his case.
It seems to me that he’s avoiding the question, because he switched from “propriety, good behavior, righteousness and Gan Eden” to what a beis din would say.