An apparatus includes a shaft assembly and an end effector. The shaft assembly includes an outer sheath and a staple driving mechanism. The end effector includes a staple deck, an anvil, a first staple driver, and a second staple driver. The staple deck defines a plurality of staple openings in at least one annular array. Each staple opening in the plurality of staple openings houses a staple. The anvil is configured to actuate relative to the staple deck to compress tissue between the staple deck and the anvil. The staple driving mechanism is configured to actuate the first staple driver to fire a first staple of the plurality of staples against the anvil. The staple driving mechanism is further configured to actuate the second staple driver independently of the first staple driver to fire a second staple of the plurality of staples against the anvil.