Now that you have the tumbler out of the lock, I'd like to address putting it back in. The first instinct is to set the cock over the square and use the tumbler/cock screw to force it onto the tumbler. That might work, but the chances are, you'll break the screw threads off in the tumbler.
What I do is press the cock onto the tumbler using my machinist's vise and some used abrasive cloth for pads. Once the lock is assembled, I place the cock on the tumbler square as best as I can, and then use the jaws of the vise to press the cock down onto the tumbler.