Not sure of the look you are going for, however my grandmother made a banana cake that was fantastic and it was doctored from a box mix. She used a plain yellow cake and added a box of vanilla pudding. She followed the directions on the box, however she used milk instead of water. After she baked the cake and allowed to cool, she would place a layer of thinly sliced bananas on the cake in between the layers. As for the icing, she used a 7 minute icing. It does not make for a pretty cake, but the flavor was wonderful.
Go here https://www.lorannoils.com/ for a great banana creme flavoring. I use it to puch up my banana bread.
I just made this one a few weeks ago and my hubby (who doesn't like cake or fruit) loved it. He said this is the cake I have to bake for him from now on.
http://cakecentral.com/recipes/7362/carrot-cake-or-banana-cake
I threw in a handful or two of mini chocolate chips. Then I iced it in IMBC. Due to the buttery icing, it reminded me of banana bread from the oven with butter, but soooo much better. So yummy!
That sounds good and simple also. So here is another question? Say I use two very ripe bananas - 2 layer 10 round - what flavor filling? I believe using banana pudding will be overkill - think maybe something to compliment the banana.
Thoughts?
If I were the one eating the cake, I would prefer vanilla buttercream. Or maybe chocolate buttercream.
If you like a fruitier cake, I like strawberry with banana on occasion. 
Try a hummingbird cake (recipe easily found online). Has bananas, pineapple and pecans, and is devine. Cream cheese buttercream would be good too.
Cream cheese icing goes well with banana cake as well, or at least for the filling. The mickey cake in my pictures is banana cake with cream cheese frosting. It's more of a spice cake that's really heavy though and the recipe's a bit of a pain. If you want to see it, send me a pm
So instead of using like pudding or preserves, use icing between?
Absolutely, if you want to! In fact, my entire life I have only eaten and made cakes with buttercream icing in between the layers. It wasn't until I started reading cake forums that I realized most of the time a "filling" referred to preserves, pudding, twinkie, bavarian cream, etc.
I like just plain ole good icing!! 
But you do have some great suggestions on this thread for other ideas.
Google Paula Deen's banana cake. I found it in a cook book (I don't have it with me right now). It's very good and moist. I used a little less bananas than what it calls for and it still turned out really good.
The buttermilk banana cake on here is so good with peanut butter buttercream. I make this combo alot as it is my kids favorite. Here is the link to the recipe.
http://cakecentral.com/recipes/2381/buttermilk-banana-cake
Another tip...purchase extra bananas and let them ripen until the skin is very spotted (brown) and almost soft. Place in freezer then when ready to use just "slide" the fruit out into bowl. The banana will be very ripe and sweet. There will be a lot of "banana water" that you will need to discard. This is just extra liquid from the fruit and is the reason that the flavor is so concentrated.
Peanut butter buttercream.
http://cakecentral.com/recipes/6804/peanut-butter-buttercream
It is so good. I just used it on a choco cake for my son. This is also the one I use for the banana cake.
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