A Conversational Strategy That I've Been Trying That Isn't Working Out.

I gave this a try, but am about ready to quit.
  1. There are a couple of people in my life who consistently interrupt me while I'm talking.
  2. I've started saying "Oh, I'm sorry. I didn't mean to interrupt you" when they interrupt me.
  3. My hope was that they'd realize that it was THEM who interrupted ME and stop doing that.
  4. They are simply clueless that they're interrupting me.
  5. I'm frustrated.
  6. I feel like it would be rude to say "Please stop interrupting me" because I was raised to not say that kind of thing.
  7. Thoughts?