Julia, here are two things that seem to pop out at me: flour and time
I did a quick survey of other banana bread recipes and yours is accurately doubled in all aspects except flour.
Single loaves typically have:
2 eggs
1 C sugar
1-1.5 cups of banana (~3 medium bananas)
2 C flour
3/4 to 1 cup of fat (butter, sour cream, etc)
1 tsp baking soda/powder (1.5 tsp if only one rising agent is used)
All recipes were baked at 350 for one hour at least.
Yet your "double recipe" uses only 2.5 cups of flour, when the pattern seems to indicate 4 cups of flour would be used. More flour would add more gluten and structure to the finished bread. It may be rising due to the baking soda or baking powder agents, but perhaps there isn't enough gluten to keep it risen?
You could try a test loaf with half the recipe and increase the flour from 1.25 to 1 3/4 (or even 2 cups) to see if that makes a difference.
A good way to check if the bread is done is to look at the sides. They should have pulled away from the walls of the pan.
The type of pan will also make a difference. While I like how easily they pop out, I don't like how the crust finishes with silicon pans. Cranberry works out fine, but the banana doesn't develop the right crust for me.
Anyway, that's my take on it. Good luck!