The cookies turned out very nicely indeed! I've included a picture, below. They are sweet, but not cloyingly sweet as some cookies are (and I'll be frank here: I like cloyingly sweet cookies), and that's a good thing because these are for my Mother-In-Law, who is a diabetic, and needs gluten-free foods containing no dairy. In total, each cookie has 9 to 10 grams of carbohydrate. That means she can have one or two with a cup of tea if she likes.
I'm going to make them again using Bob's Red Mill Gluten-free Oatmeal, which I will put in the food processor first to break up the oats. I'm also going to see what happens if I use apple sauce instead of bananas.
I think these cookies will become a regular part of my cookie repertoire. My family seems to like them.