Well remember you are slow cooking and applying moisture thru spritzing and foiling, so a shoulder roast may not be totally out of the picture. I use either Underblades or 7 Bone. 
under blade pot roast = bottom chuck roast =   California roast = under-cut roast  Notes:    This cut is tougher than a top blade   pot roast, but it's flavorful and economical. It makes a   fine pot roast, but it's too tough to roast with dry heat.  A steak cut   from this is called an under blade steak.   Substitutes:  7-bone   pot roast OR top blade pot roast.
7-bone pot roast = 7-bone roast = center cut pot roast =   chuck roast center cut  Notes:   This is a tough cut   of meat, so it's usually braised   or cooked   in liquid to tenderize it.  A steak from this roast is called a 7-bone steak.    Substitutes:  arm roast OR blade pot roast.
I have had some of these same cuts pull easily, some pull partially and some not pull at all. Once I started doing the foiling around 160 and taking them to a 210 internal finishing temp, I succeeded alot more.