In your situation I would have an out also, but I may rule differently depending on how close to the bag the obstruction took place and if that may have had an influence on the runner sliding past the bag.
Example, 3B obstructs the runner about two feet from third base. The runner, in trying to avoid the collision which is their responsibility, has to slide past third and reach out with a hand to grab the base. Runner gets the base but can't hold on and is then tagged, I probably wouldn't have an out here as the obstruction was a main cause of the runner sliding past the base.
Go ahead and correct me..
