I think the higher temp that most shoot for is to aid pulling. Around here, most of the old school bbq restaurants serve chopped butts; it's the Lexington, NC style and it's usually smoked to 180° to 185°(not that they measure it). At that temp, the bone will usually pull right out and you can easily separate the different muscles and then chop with a cleaver. After chopping, the results are all mixed by hand so most bites have a bit of bark and some of each muscle.
Eastern NC/SC style whole-hog bbq, it's pretty much impossible to get all of the hog to pulling temp without overcooking something so they manage heat distribution, cover quicker cooking sections during part of the cook, and look for 180° or above everywhere. After separating the ribs and other cuts for serving separately, they chop everything else and mix it all together (including some bits of crispy skin) so that ask the different textures and flavors and degrees of doneness are ask blended together.
The point of this is that you might wanna try stopping the cook at the point you describe above and chop instead of pulling. It's still very tender but has a different texture and mouth feel than most pulled pork.
My 85 year old mum usually complains that pulled pork is stringy; she eats it anyway.