Well I found this "odd" strafe a long time ago but completly forgot to show it.
Well bassicaly is jimmy with one of his arms down and the other one up like if he was gonna stab someone.
If you look carefully at hal or norton (or any other modded character including jimmy) short strafe after using the bearhug you will notice that it looks the same. Like at the end of johnny main boss combo (the overhead stomp combo) he has the same strafe as his beta style.
Maybe this was supposed to be their original strafe but they ended up having the same as the grappler jocks ones.