I'm not sure if this will help you or how it is related exactly, but I thought you, and the forum, would find it interesting.
So my Spanish teacher has a Portuguese Dad, Mexican Mom, and lives here. From what I can tell, she speaks Spanish, Portuguese, and English fluently. I asked her what language she thought in most and she said Spanish and she thinks through the other languages. But, to me, her English seems so fluent she has to think in it sometimes.
My French teacher (who I personally think is amazingly lucky) was born in Spain to an English-Spanish mother and an American father. She grew up in the Catalonia region and went to a French High School. She speaks Spanish, French and English fluently, and claims to speak Catalan, but I've never heard her. I asked her the same question and said that for the most part while she's been in America she thinks in English and thinks in Spanish in Spain or with her spanish-speaking friends. She said she has to think through French but she couldn't tell if she thought through it with Spanish or English. (I don't know, is it possible that she thinks in French but isn't entirely comfortable?)
Just thought I'd give you more examples of processing.