Can time-related words grammatically modify prepositional phrases?

1. Two years into the eight-year sentence, he committed suicide.

2. Two years into the program, we had virtually a 100 percent compliance rate

3. An hour after Ben arrived, I passed Ralph in the hall.

I came across these three sentences in some English books.

I don't have difficulty in understanding what the sentences mean, but I'm not quite sure whether "two years" in 1 and 2 modifies "into the eight-year sentence" and "into the program", and "an hour" modifies "after Ben arrived".

I think "two years" and "an hour" grammatically modify "into the eight-year sentence", "into the program" and "after Ben arrived" in each sentence.

Am I right?

Lastly, are all the sentences grammatical and natural?

Thank you very much!