Up two and defending and "intentionally" fouling can work if the other team has plenty of time and shoot the three very well. It will give us the ball back with at worst tied in most cases. And if there is enough time left that we can run stuff if tied that might also work. What I fear is the opposing team making the first and getting the board on the second and hitting a two or a three with little time left. I am not sure how the analytics play out on this.
Being a top defensive rebounding team not only limits the extra possessions your opponent has but allows you to outlet the ball and get on the fast break quickly turning defense into offense. Theoretically, I agree. Practically, I disagree. Rebound-outlet-to-fast-break hasn't really existed as a style since the 1980s. That's not to say we won't ever get one, though.
For many years we sent all five to the defensive glass and had guards being the best rebounders. Not the way to start a fast breakl You need big glass cleaners to get defensive rebounds and then pass out.
Rebounding the 2nd miss was my first thought. I would be very careful doing this against an extremely good rebounding team