Answer
In a confirmed, IFS-investigated case, this turned out to have nothing to do with replication of persistent custom fields at all — the underlying cause was specific code changes needed in a custom Event being used alongside the field. This is a useful negative-confirmation: persistent custom fields aren't inherently blocked from replicating between Satellite and HUB environments, so if you hit this symptom, look at the custom event/logic layered on top of the field rather than assuming it's a fundamental replication limitation.