Part of the problem could be the refreezing of the ice cream. You know when you take out ice cream, eat at it for 5 or 10 minutes and then put it back in the freezer...and then the next time you take it out, some of the ice cream is a little icy and bit grainy?
I'm not sure you can solve this if you use the same recipe. Instead, I would recommend using the highest fat chocolate milk you can find instead of using melted chocolate ice cream.
I really doubt the pudding didn't get dissolved completely. If that really was the case, you could heat the mixture before you put it in the pie crust.
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 Industrial Product
By way of example, this is the list of ingredients from Jello Vanilla Instant Pudding and Pie Filling mix (a very common brand in the US):
The ingredients that are not well known, or are that are relevant to the texture are:
Modified cornstarch. The label does not specifically say how the cornstarch has been treated or modified, but it is likely that it is pre-gelatinized which is what allows it to be "instant pudding", thickening with the addition of cold liquid.
Disodium Phosphate. Anti-caking agent. This allows the mix to flow freely after storage.
Mono- and Diglycerides. Emulsifiers.
Tetrasodium Pyrophosphate. Per Wikipedia:
Note that this both emulsifies which helps create smoothness and uniformity, and thickness.
What you do not see in the mix is any true dairy or egg products. The pudding is entirely a creation of these thickening agents, and the flavor only from the natural or artificial flavors (which might or might not include vanilla extract, but more likely are vanillin and other flavors).
Home Production
Puddings (at least in US usage of the word) are a variant on custards, where the thickening power of eggs in a basic custard is supplemented with a starch.
It is not really possible to achieve a consistency identical to that provided by the industrial ingredients, so if you are using that as your standard, you will fail.
Still, an extremely smooth product with a delicate mouth feel (which in my personal opinion is actually superior) is possible by creating a pudding based on:
The ratio is very very approximately: 1 quart (1 liter) dairy to 6 eggs yolks to 4 tablespoons cornstarch.
These puddings can be created stove top or baked in the oven, and can be flavored in a variety of ways. In either case, you must use good technique to avoid curdling the eggs.