That is basically how I make my shredded beef when using chuck. Sometimes you have to cook it longer until the meat gives up. At around 195°F, you should do a fork test; which is to unfoil the roast, insert a fork and twist. If it twist easily, it is ready for pulling. If you can't twist the fork, or it twist with difficulty, re-foil and continue to cook until it reaches a point where the fork will twist. So that would mean to check it at 200°F, or 205°F etc.
As for the texture, I've always found pull beef to be a bit on the dry side, and I will add either some low sodium beef broth, or Au Jus, or one of my favorite sauces; to give it some moisture. Once while making a pulled beef sandwich I used Italian dressing, and that came out great.