I still can't get the choke to push back in - and when you push the stop button, the choke usually goes in with it - but I physically can't make either of those things happen. Because they're both plastic, I don't want to force them either.
Here's a pic with the choke out as far as it goes and the saw in the run position:
Here's a pic with the choke in as far as it will currently slide and the stop button down as far as it will currently go. The difference between the photos is subtle - but the choke will go in about 1/8". It doesn't look like the stop button is making proper contact either.
Here's the best shot I could get of the blue choke bar where it meets the carb without taking it all apart. It still looks attached to me.