You might be overthinking it here. Sure, the logic looks sound when it comes to choosing perfective over imperfective. The thing is the logic behind that sentence is not to question perfective or imperfective aspect of the action, but to show if the action was or was not taken. In other words the speaker does not care if the article was read fully or not, they only care if it was read at all at any capacity.
That's probably why, as noted by @Soft sign, you can use either aspect of the verb with little to no difference in meaning there.
Looks alright but you forgot to put занят in the past there. It should be "был занят", without был that part of the sentence refers to the future (even though it's technically in the present tense) and the clause is in the past. I'm sure you now see why it looks funny the way it is.