What's the best way to execute a pulled pork dish?

You definitely want to pill the pork apart with a pair of forks or your fingers. The best way I find is to allow little "clumps" of pork to permeate the mix. Note that while books talk about cutting against the grain of meat, that is for raw or cooked meat meant to be sliced and served. The reason you cut against the grain in that situation is to tenderize the meat by cutting the connective tissue. In the case of pulled pork, the connective tissue is already broken down and dissolved, so you will have a tender product even when you are pulling with the grain.

Personally I do the pulling with my fingers. Makes it easier to pick out any gristle, veins and fat.

You need to cook the meat until it's basically falling apart on its own. And you need to cook it for a long time over low heat -- high heat will cause it to toughen up.

Once it's cooked, you should be able to pull it apart pretty easily with your hands, or with a couple of forks. If there are bones, you should be able to easily pull them free of the meat without any significant effort. Once it's bone-free, if you're in a rush, you can just smash it down and it'll start breaking apart into fibers, although not quite as much as if you were to pull it. (and as Doug mentioned, you then can't pull out the globs of fat and such).

I'll often use a mixed technique -- break the meat (typically pork, but also sometimes chicken) into larger chunks, exposing some of the middle, and let those cool down some while I'm shreading another chunk. If the meat's allowed to cool too far it won't shread easily, but if it's too hot it's uncomfortable to work with by hand. You can always use the two-fork method (hold one in each hand, reach into the meat, and pull them apart, tearing the meat), but I find it to be slower... and I'm not a fan of the blobs of fat and such.

Once it's shreaded, I'll put it into a container and top it off with whatever liquids were extruded during cooking, so that it remains moist. If you don't, the exposed hot meat will exude a lot of steam and dry out.

Chopped pork is not an uncommon thing to see in Southern barbecue. Though it is largely in whole hog barbecue. With whole hog, you have to cook the tougher cuts a little less than desired, in order to keep the cuts with less connective tissue from becoming overcooked.

If you want some unsolicited advice, I would suggest giving your roast another hour of cooking time, so you can pull it apart more easily without the help of a knife. BUT, there is absolutely nothing wrong with how you are doing it, especially if you are happy with the result.