Chloe You can find records for Zychlin online in the Polish Archives. I do not know where you can find records for the Book of Residents as I too found family indexed online at the jri-pl site.
You may also be interested in the Zychlin Memorial Book. I received this notification-
We are pleased to inform you that the translation of the Zychlin Yizkor book translation has been completed. All the chapters have now been posted online: https://www.jewishgen.org/yizkor/Zychlin/Zychlin.html
Scher (Lithuania Latvia) Berman (Lithuania Latvia) ) Blum Lithuania and Latvia)
Samuels (England and Wales -name in Poland Trzmil from Zychlin) Kaplan (Latvia)
Dembinski Zychlin Poland Kohn Zychlin