You can add some baking soda to the original recipe (1/2 c. juice or slightly less). Baking soda is alkaline (or a base if you're a chemist). It will neutralize the acid (source of tartness sensation). THOROUGHLY stir in less than 1/8 teaspoon at a time until the tartness is reduced to the level you wish. Be careful as too much will remove all the tartness and therefore the taste sensation the lime juice adds.
It is difficult to give an authoritative answer because who knows what a "typical" pie might be like. It might be different for every person you talk to. I will therefore answer just for myself.
All of the made-from-scratch pudding pies that I have made have been very similar- a lot of sugar and fat and some starch to make the gel. Usually recipes also call for egg yolks which also help with binding but make the pudding a little more custardy instead of just a gel.
The texture should be sliceable so that the sliced edges sag but don't flow. I have had pies that have to be scooped out which, while perfectly delicious, isn't as nice a presentation. On the other side of the spectrum is what you have- rubber- which is a great presentation when cutting but not much fun to eat.
Gradually adding your corn starch slurry is always a good idea. Often the starch is mixed with the sugar to make sure it is evenly dispersed and then added to the liquid. As long as you didn't have clumps your technique here was fine.
I don't think your expectations of a banana pudding pie or your technique are wrong. What I think is slightly wrong is your expectations for this recipe. It's "wrong" to call something a "take on a southern classic" that uses soy milk and organic margarine. The milk fat and egg yolks in typical recipes do a lot to make a smooth, custardy pudding. Doing this with different fats and soy milk could be good but I would expect it to be different.
The bananas don't have to be precooked- that would be horrible, I haven't used earth balance but if it behaves like normal margarine then your crust sounds like it is pretty normal. The number of bananas also sounds reasonable. You want a good layer but not so much that the pudding can't work in to bind it together.
Reducing the amount of corn starch a little should make the filling softer and more to your liking. You could try adding a little more fat which will also soften the pie. In the end though, I wouldn't expect a typical texture of a pie that is made completely of non-typical ingredients.
Best Answer
The serious eats article that accompanies this recipe does a good job of explaining what you are trying to accomplish.
You are trying to have wheat gluten that is interspersed with pockets of fat. The fat pockets are tender, the gluten is flaky. Perfect balance.
They dough that you have doesn't have any gluten development and is basically shortbread. If you press it into a pie crust it will be tender and flavorful but not flaky. It's still delicious so don't throw it out- it just won't be perfect.
There are three ways that you could have too little gluten:
The recipe calls for all purpose flour. It needs to have some gluten but not as much as bread flour.
This recipe calls for some of the flour to be completely blended with the fat and then flour added in a second stage and only just cut in. If this second addition of flour is too thoroughly blended into the fat you get shortbread.
The recipe calls for resting the dough for at least a few hours and up to a few days. This is important. Only some of the flour in the dough has access to water to form gluten. The dough needs to be given time to rest to allow the flour to hydrate.
I love this pie crust recipe. It turns the traditional method on its head and it works very well. It has fewer tricky points for failure than the traditional method but it still helps to know what you are doing.
I highly recommend reading the article that accompanies the recipe.
http://sweets.seriouseats.com/2011/07/the-food-lab-the-science-of-pie-how-to-make-pie-crust-easy-recipe.html