[sfbbqguy]

I think you're right on at 225*.
If it was me I'd use beef broth as injection...unless you want to get fancy and add some other spices and stuff. Inject small amounts in many places.
I'd likely add more beef broth instead of the apple juice when you wrap.
In the case of this small piece of meat maybe you should wrap earlier than 160* as you don't want it to dry out. Once it has gotten some smoke you should be able to wrap...think I read where 130 is about where it stops getting much smoke.
Let it get to room temp before you throw it on. Cook it 'til you can probe it and get no resistance...like budda.
Like Lando said it's going to be faster than you think.