I think that it can work, actually. Added now.
"Jestem tak samo" doesn't make sense grammatically. "Jestem taki sam" would be "I am the same" and at least on an interpretative level it suits the meaning.
"Jestem jednorodny" sounds like something from chemistry, if chemical substances could speak ;) I guess that would be "I am homogenous"? Or "I am uniform"? Super weird.