One of my pet peeves, especially since it's hard to see why it's hard. People who would never say "John gave it to I" are suddenly at a total loss when faced with a compound subject or object. Seriously?
All I can surmise is that their parents talked that way, and their teachers never taught them to practice saying it correctly. As you hint, all one has to do is to substitute a singular subject, and the correct object just falls into place naturally. If the student is taught to do that - to think about the sentence as if the subject were singular, rather than several things, the answer is obvious.
It wasn't by accident that I used the name "Brian" in my example. Brian Kilmeade on Fox & Friends makes that error all the time. Therefore, he sounds like a dunce. And, now he's written a book! Who knew?