Solution 1:

Yes, the simple "I read the book" usually implies finishing it. There's enough ambiguity in the usage, though, to enable some intentional duplicity:

"I know you need to read To Kill A Mockingbird for English class. Did you read it today?"
"Yeah, I read the book."
"Great, what did you think of the ending?"
"Wellll.... I read the book, like, I read some of it, but I didn't finish it...

This would generally be seen as a misuse. However, you could add a qualifier like a time span that might shift the received meaning to non-completion:

I read the book for two hours today.
I might have been bored on the plane, but I read my book.

But no, shifting from simple past to past perfect does nothing to influence a sense of completion, for any task I can think of ("I fixed/have fixed the car," "I cooked/have cooked dinner"), though continuous tenses certainly can ("I'm reading the book").