Here are some thoughts:
First, consider what we notice in common about every time Iago gives a monologue:
1. He reveals to the audience what he is going to do - or - he reveals the truth about what he has already done.
2. He demonstrates the evil and immoral of his character while when we see him talking with others, he works hard to manipulate them from believing he could be anything but innocent.
Another aspect I would consider if you stage it beforehand is the fact that prior to talking to Roderigo, he must have heard something about Cassio's appointment to the new position. This would be a monologue full of jealousy of Cassio and anger with Othello for not having given him the position.