With the tang broken your not going to get it any deeper.
I've replaced them by grabbing the part that is sticking out with
needle nose pliers or vise grips, depending on size of helicol, and pulling straight up. Helicoil will stretch and come out of hole, hole will need to be re-tapped and new helicoil inserted with tool.
If most of the helicoil is in the hole and only a small amount is sticking out and you need to do a "quick fix" just file or grind off flush to surface.
Tom