This, and other answers in this vein, are correct.
There is no absolute 100% foolproof target temp to take pulled pork to where it shreds. It shreds when it shreds. I’ve had pork shred at 190. I’ve had pork not shred until 200 or slightly more. If I had to pick a number, 197 is a good one, but USE YOUR SENSES! This ain’t rocket science, you don’t need probes and gadgets to figure out when its done. It’s done when the following holds true:
- The meat slumps upon itself
- The bone can be removed with little to no resistance
- A fork inserted into the meat twists with little to no resistance
That’s it. The meat is done when it tells you it’s done.
It’s quite possible your thermometer is off. My own digital thermometer, for example, reads about 4-5 degrees high. (Just stick it in boiling water to get a rough idea of how off it is. If it’s well off 212, well, there’s your problem.) The only reason I ever probe my pork shoulder is to get an idea of how far along it is. I do not ever pull it based on temperature. Never ever. I pull it when it feels right.
That said, I tend to prefer chopped pork to pulled pork, so I generally pull it before it becomes shreddable when I’m making it for myself. For parties, I take it all the way.
I do a typical pork butt in 6-9 hours in the smoker @ 250-270. It’s shreddable, it’s soft, it’s juicy. You don’t have to sit around for 12-14 hours for it to be done. In fact, I prefer slightly higher temps, as I swear the pork tastes juicier to me, and it’s got a better bark. The OP’s timeline is not crazy off and should yield a fine product, although I never foil my butts while cooking. (I will very occasionally foil a brisket.)
As for rest, I’ve done it with no rest, but 30 minutes to an hour wrapped tightly in foil in a cooler seems to do well for a butt. But I typically only do that when I have to hold it. Otherwise, I just serve it as soon as it comes off the smoker.
Seriously, just use and trust your senses. If it ain’t done, it ain’t done. Give it time. And nothing wrong with your time (other than not waiting long enough) or temps.