Seriously just get the neck nice and wet with something slippery like soap or star san. put a thin washcloth in the carboy (holding onto a corner outside!) Bounce the stopper on top of the cloth and pull. Eventually you’ll get it into the neck and then out.
You can also fashion a coat hanger hook if that’s more your speed.
drape a thin cloth into the carboy, keeping the four corners of the cloth “out”. Then manipulate the carboy so the the stopper is near the neck. Then pull the cloth corners… kind of lassoing the stopper and pull.
The other person made a tool, kind of like a toggle bolt. With wire he made a loop, small enough to fit through the hole of the stopper and then with the loop thorugh the center of the stopper, placed a pice of wire to prevent the loop from pulling back thorugh, and pulled the stopper out.
I finally got one of these after you or someone else posted the same advice in a similar thread, and indeed, thank you. A very small price differential for something much easier to deal with.
Thank you everyone. After the beer was done fermenting, I used the plastic bag trick and it worked first try with no effort. (And I bought the universal stoppers!)