HI guys, Not sure if I can help you but maybe you can help me. I have taken a vertical pull starter off from a Rover ES200 mower fitted with a B&S model 92508 vertical pull start. A similar problem to yours that the starter does not work as well as it should. I do not have a manual or a picture of it to work off but I have a part that I do not have a place for which was rattling around inside the housing. I guess if it is meant to be there (not just thrown in there at some time) it would anchor the friction doo-dah somewhere, but the only place I can find where it might fit is under the pull rope guide but it is too long and hits the rope spool.
It may be bent? Hopefully I have been successful in attaching the picture
If I can get a large enough hammer it will run for awhile just trying to get away from me
