HA!
I figured out a flaw in the system. An exploit if you will.
You can completely bypass the "Attempt Introduction" method. All you have to do is go to Strangerville and wait for them to show up. The bar and library are good for that. Once they show up, the famous sim will always have the "Talk about Strangerville" option that EVERYONE has in that town. Just select that and you'll get some friendship points. Then, it's just a matter of using the normal interactions that now show up!
I was playing through Strangerville again with a new sim and the Celeb I've been trying to interact with showed up right away. I tried "Talk about Strangerville" and saw the points show up. A lot of new interactions were available after that.
