Sure, beef shoulder (chuck or clod) can be cooked hotter in the 275° to 300° pit temp range. I hope you could get thick ones, they are easier to cook. If you are going for pulled beef, chucke do benefit from a wrapped finish.
Parchment paper has a release agent, so it might not be your best bet. There is a 'natural' parchment paper out there, but it is hard to find.... so maybe foil will be your best bet.
I tend to late inject mine when they get to an internal of 160°, and then I wrap (adding some more juice to the foil) and cook tender, then rest in a cooler for an hour or two.
Here is my current beef juice I use on brisket, chuck or prime rib. It a modified version of juice that RRP turned me on to. If you don't have all the stuff, you can wing it.... your goal is a jazzed up beef broth, strong on the beef flavor, but not too salty because if you do a late injection there is not a lot of time for the salt to cook down.
RRP AuJus - ~thirdeye~ version for AuJus or Injecting
(My version begins with beef consume for a deeper beefy flavor, uses dry onion soup mix, and more water as the consume is saltier and thicker than beef broth. I went heavier on Wooster and added soy sauce to increase the umami*, and added a couple of other ingredients).
1 14 oz can Beef Consume
1 packet Lipton Beefy Onion Soup (dry mix)
1-1/2 of the soup can cold water
5 teaspoons Worcestershire sauce
2 splashes of Soy Sauce
1 teaspoon of garlic salt
2 teaspoon Herb-OX beef bullion
2 teaspoons Montreal Steak rub
1 teaspoon Smokin’ Guns Rub**
1/2 teaspoon celery seed
1/2 teaspoon black pepper
Bring ingredients to a low simmer in a saucepan, and cook for 15 to 20 minutes. Try to avoid having the liquid come to a boil. Additional water can be added if flavors are too strong, or if liquid gets too thick. AuJus is a thin table sauce, NOT a gravy. Pour through strainer to remove the onions and coarse pieces from the Montreal Steak rub. Serve warm as an aujus, or use as an injection.
Any leftover can be frozen in small containers or an ice cube tray to use later on...