I would push and pull it and pan it up in a big Sams disposable pan. Add some liquid (see below) and a liberal dusting of the rub you used to start with. Put a tinfoil top on the pan and heat to 160 on the pit on in the oven. You want just enough liquid to moisten it but not enough for the folks to notice its been sauced. Simple huh? I would go something along this line but surely feel free to tweak it to your own taste buds.
2 cups bbq sauce (Headcountry Regular works well)
1 cup apple cider or juice
1/2 cup black coffee
1/4 cup apple cider vinegar
2 T. Wooster
1/3 cup Jack Daniels or Ezra Brooks
1 T. dry mustard
1 T. Hotsauce (I like Sirriachi or Franks)
2 t. MSG
Get it mixed up and simmer a while in a small sauce pan till the flavors get blended. Dump on the pork and mix it up a bit prior to reheating. Sample and add rub, salt and peppa as needed.
bigwheel