You probably are correct in now needing to pull the motor and at least remove the head to examine #1 cylinder for damage and to remove at least plastic pen parts. It looks odd that the #1 butterfly got broken, but seeing that it did, you likely do need to examin further for damage. Perhaps now that the carbs are off, you can examine the inlet to the motor and see if any parts made it there and got stuck before entering the chamber.
Regarding your carb "dirtiness" condition: They don't really look too bad and a bit of soaking and careful elbow grease should remove the accumulations. If you haven't already, be careful removing the float pins from the posts in the carb body, as those posts are very easily broken if the pin is stuck. (I know from experience on mine.
) I found that lacquer thinner worked good to remove deposits from gas that sat too long in the bowls. Your #2 likely was dry as it sat so nothing deposited in it. The stuff left on the float bodies (a hard plastic foam on these models) after some cleaning shouldn't be a problem - its hard to get it all off them. I'd remove and carefully clean all the jets, making sure that the tiny holes are all clear. (Use a fine soft copper wire to poke the holes, being careful not to damage the brass material.) With your low mileage, they shouldn't need replacing, but all the o-rings should likely be replaced. You might want to consider getting new float valves, as they tend to be hard to clean and any leaks from them will overflow the carb to cause gas to spill out the overflow.
