Alternatives suggestions to apples and bananas
For an applesauce substitute you could make any other fruit sauce using the same method as you would make homemade applesauce - pear sauce, peach sauce, etc. In my experience applesauce is always a bit of a variable in recipes depending on if its store bought or homemade given the different sugar and water content. Baked goods made with homemade applesauce turn out sweeter and have this wonderful soft sticky crust. This happens because I cook down my applesauce, thus increasing the sugar content.

Along the same line I would use a very reduced fruit sauce for a banana substitute for baking. Bananas have tons of sugar in them, so the high sugar content is ideal.

With either replacement you should play around with how much you cook down your fruit sauce and experiment with different fruits. Water and sugar content of fruit is never exact by recipe standards, so you shouldn't have too much of an issue swapping fruits.

If bananas are primarily used raw as a sweetener, like in smoothies, try dates which have a similar sweetness.