I know this is an old post but I'm looking to do this same repair on my Atari 800 that I just dragged out of my mother's basement and refurbished. Everything was going well until one of those plastic posts broke off. I was quite annoyed! After much searching, I found this post and I tried to muster up some courage (about 2-3 months now) to attempt this repair. Just a few days ago, I stumbled across this video:
Obviously, this doesn't show how exactly to repair those pieces on the Atari but it got me thinking how I could use this method to do so. I keep looking at the broken part(s) and trying to come up with a plan. So far, I don't think that it will look exactly as it did but that won't matter since those pieces are completely inside the case. I'm even contemplating using some sort of hybrid method that includes melting a pin into the plastic as well but still thinking it through.
I'll update this post with my results and try to post some pics in the hopes that it will help someone out.
EDIT: If you have any thoughts on anything related to this repair, I'm all ears!