Basically do the same thing your thinking, but when you make the "tube" shape for the blue fabric turn it so the seam allowance is on the inside. And make it one whole piece with no extra hanging out. Then after sewing the ends together, handsew the gloves onto them. It works really well. That way too its easy to replace the gloves if they get dirty. Does that make sense? I feel like I'm gonna confuse you.
I think I understand. If not, I'll be back.
Thank you for the quick response!