How would you handle this?

[chuck chopper]

I would assume the base umpire making the DDB signal is also responsible for overruling the plate umpire. During the play if I was the base ump I would make darn sure my plate umpire buddy saw me holding my arm out so that whatever he/she calls at the plate I might over-rule. Actually if when the runner rounded 3rd I felt the Obstruction should be dropped then I would have also made sure my plate umpire saw me "drop it" so his/her call at the plate would stand !