mmm, well, I think you are going about it the wrong way.
Saying the other two boys are "joined at the hip", and the others are "hangers on", and you are not even ever inviting anyone because of this.
Sounds like a negative way of looking at things.
To GET invited to things, you have to start out by inviting people to yours. that is how life works for most people.
There is no fixed hierarchy with boys this age, in my experience (I have an 8 yr old boy and an 11yr old) and friendships and popularity fluctuates.
A positive step to take would be to just invite a few kids.
I feel you are taking this way too seriously, the friendship issues at this age. So maybe you invite someone who says no, so what? Or maybe you invite someone and it's not a success, so what? That si all part of it.
Been there done that 
relax about it, and just invite a nice kid every now and then and see where it takes you both.