An assembly is provided for an aircraft propulsion system. This assembly includes a fixed structure, a translating structure, a blocker door and a folding linkage. The translating structure is configured to move between a stowed position and a deployed position. The blocker door is pivotally attached to the translating structure at a first pivot joint. The folding linkage links the blocker door to the fixed structure. The folding linkage includes a member pivotally attached to the blocker door at a second pivot joint that is radially outboard of a skin of the blocker door when the translating structure is in the stowed position. The second pivot joint is radially outboard of the first pivot joint when the translating structure is in the stowed position.