The first thing I would do is check your router armature and the bit you were using to see if they are bent. I would surprised if one or the other is not after seeing how much force the ejected piece had. You have already realized that your 1st mistake was feed direction. Your second mistake was "capturing" the piece between the bit and the fence. There is no give that way. There is also nothing to stop the piece from diving into the bit which will ruin it. Personally, I would have done the rabbets on my jointer, does a much better job and faster. But this is a router forum so in that context, I would have done the shorter rabbet first. Then I would have taken a small portion off of the second rabbet leaving enough wood on the piece to keep it stable. Then I would have cut a strip of wood the thickness of the piece you cut off the first rabbet and used it to keep the piece stable while I finished the second rabbet. Last, I would have flipped the piece over and done the bullnose. You could put a drop of glue at either end of the support strip to keep it in place while you are finishing the 2nd rabbet.
There was a post about a month ago from someone who had tried to rout something in a way that he knew wasn't safe and he injured his hand badly in the process. After he got hurt he rethought his job and came up with a safe way to do it. If what you are doing seems like a bad idea, then it usually IS a bad idea. If you can't figure it out, ask for help. I have offered one way, there are probably more coming.
By the way, you made some really nice looking stair nosings.
There was a post about a month ago from someone who had tried to rout something in a way that he knew wasn't safe and he injured his hand badly in the process. After he got hurt he rethought his job and came up with a safe way to do it. If what you are doing seems like a bad idea, then it usually IS a bad idea. If you can't figure it out, ask for help. I have offered one way, there are probably more coming.
By the way, you made some really nice looking stair nosings.