You can kill crota with swords if your team downs him twice for each sword. If you dont get him killed in two swords a third may be needed and crota will spawn in oversoul, during thus time provided crota is low on health your team should only be focused on crota so your SC can take him down thus killing crota and canceling out oversoul.
On the final sword run, the SC hits him till enrage. Then we take crota down again while the oversoul is active. However as soon as his life bar is empty he gets a shield. The killing blow isn't killing him, its just erasing his life bar and giving him a shield, which is the problem.
We have even shot the oversoul after taking down crota but still he lives.