I'm a US immigrant one country north of you. It is definitely a process to integrate and live in harmony in a new culture, but I didn't find it "excrutiating." More an exhilarating adventure.

I didn't "extract" my core values. I reevaluated my non-core values. I bent some. I jettisoned others. I added new ones. The resulting me on the other side of this never-ending process is very different than the me that started it. But my core values remained.