Okay, let's not get ahead of ourselves. Do not add the pureed beans to the chili until the meat is fully tender. This is a finishing step. Once the meat is fully tender add the beans. By tender, I mean that some of the meat will be breaking apart but some to most cubes will be intact, but almost ready to fall apart.
My second finishing step is to add corn tortilla crumbs. My local HEB happens to sell them. If your grocer does not, you can simply grind up some tortilla chips in a food processor or blender. I do not measure just how much, but it is probably a 1/4 cup that ends up going in. This will further tighten the broth and thicken the chili to the point where it will be perfect. The tortilla crumbs also add a very nice earthy back-flavor to the chili.
Primo Oval XL, BPS drum, Weber gasser