Looking at the last picture, your measurement looks like it is stretched. Your zero is not nearly on center with the pin, nor is the 6, or pin edge to pin edge. A new chain is relatively cheap. I'd also say that your chainrings ARE worn. Just replace the big ring.
I am going to do exactly this on my commuter when I get a chance as I also experience skipping, and also have had the chain completely slip off the front a few times. I just need to look for a new 48t 110bcd ring, which shouldn't be hard to find as they were pretty standard.