I don't understand why this is under debate. Any property used or sold by Jeremy before his conviction was his as the sole heir. That right may have been removed by law, but only after the fact.
Interested-observer, it's good to meet you. May I address you as IO, please? It sounds as if you are saying that on death of his family, as sole heir, Jeremy inherited. The law allowed the family to take over his inheritance AFTER he was convicted. If I have this wrong, please feel free to correct me.