I have always fond Benson really helpful and have routed via their overhead on many more than one occasion. I would be surprised if you would have a problem unless of course they have conflicting activity. As always you are far more likely to receive a helpful response if you explain what you want to do and why.
Often a telephone call before makes very good sense. After all what you propose is a "special" mission. The call shows forethought, gives them a chance to think about the best timing based on their ops for the day, and means they know you are coming. From your point of view it saves a refusal in flight.
I have 'phoned before for exactly the sames reasons, albeit not Benson, explained I had some friends who lived with the ATZ, and arranged the "flight" before leaving the ground.