Knight's-Move Cell Shifts for Polyominoes

Introduction

Two figures can be tiled with copies of the same polyomino. The figures differ in only one cell. Can the different cells lie a knight's move apart? Thanks to Jenard Cabilao for suggesting this problem.

Here I show minimal known solutions for polyominoes of orders 3, 5, and 7. Cell shifts for polyominoes of even order must preserve parity, so they cannot be a knight's move apart.

If you can solve any of the unsolved cases, please let me know.