Assimilation /d/ + /j/

No, the d-j assimilation would not occur with that example. I'm not sure it happens with *any* words other than "you." For instance, I'm sure it can happen with "I heard you," but not with "I herd yaks."

Thanks, I guess you're right.

How about assimilation of /t/ + /j/ then? On the face of it, it seems to be the same thing but we use it, for example, in 'last year'..

It does sound like a t-j assimiliation is used in "last year." But there wouldn't be one in "last yak" or "last yacht" or "last youth" or "just you." I'm hard pressed to come up with a pattern for that one, off the top of my head.

It does seem to only affect the word "you": I would pronounce "Did you go eat?" with the /j/ sound, but not "Did Yugo eat?"

The /t/ + /j/ assimilation you're talking about is more of a /t/ + /ch/. "I hit you" would be a good example. I don't think I assimilate "last year," but it doesn't seem too strange to do so...I wonder why?

Why can't it be that "did you" is so frequently used that it becomes a logical word by itself? I remember my mother told me she was from Queens, where they had to take speech therapy because they would pronounce, "did you eat yet?" as "jeet chet?"

Yak and yacht and youth are so infrequently spoken that they seem to require more annunciation to be understood.

I think that what we're dealing with is "you" being used as an enclitic. This is a form of a word that only exists when connected with other words, and is unstressed. They're very common in other languages. They almost never exist in one's own language, where they're called "sloppy pronunciation." The enclitic form of "them," for instance, is "um" or "em."
Note how when the "you" is stressed the assimilation disappears.