How to make an apple pie like KFC/McDonalds

The only trick I know of is to use a different variety of apple-- some will turn to complete mush, while others stay firm. Unfortunately, unlike potatoes, they don't tend to be marked at the super market as to which variety they are.

Now, I'm not familiar with Bramley, but from what I've found, it's compared to Granny Smith, which tends to hold up well in pies.

I'd recommend blind baking your crust, if you aren't already, so the filling isn't in there as long, and possibly going with a thicker slice of apple when you're cooking, in hopes they won't break down as quickly.

update : in checking CookWise, there's a comment in the apple pie recipe that "briefly sautéing and poaching apples softens them slighly before the sugar, which prevents cells falling apart and preserves texture, is added"

What you have there is simply water seeping out of the gel and bringing some dissolved stuff with it. This is known technically as syneresis. What will help is to add something stabilize the gel. Xanthan gum is probably the easiest thing to use. You can find it at health food stores or Whole Foods because gluten-free bakers use it a lot. Start with 1/8 teaspoon pureed into your filling. Sprinkle it over the filling liquid before mixing, and put it through a sieve before baking to catch any clumps.