Best way to handle this situation.

[Andy]

I'm sure someone will correct me if I am wrong, but here is my take:

Obviously, if F5 had cleanly fielded the ball and made a play at third, it would be your responsibility.

Since the ball went through to the outfield, the lead runner touching third becomes the responsibility of the PU, the BU now has responsibility for the trailing runners and ensuring they touch each base properly.