Corner Chain

 The lack of rules surrounding shaded squares initially caught me off guard, but the special rule seems perfectly tailored to target local nonuniquenesses whilst allowing for a more free-flowing form of Mochikoro. For example, rectangles are always allowed to be 2 cells wide if necessary, but only some of the small region shapes can be used.

https://pzprxs.vercel.app/p?cornerch/5/5/3o3i4p

https://pzprxs.vercel.app/p?cornerch/7/7/6k4t.z8k4

https://pzprxs.vercel.app/p?cornerch/9/5/.i.i2q6i.q5i.i./

https://pzprxs.vercel.app/p?cornerch/8/8/j.h.g2n6zl6n4g2h.j

https://pzprxs.vercel.app/p?cornerch/9/9/4l3q4h4n4n4i34l3k4r3m3g