This sounds like an opportunity for an audio in a chat feed where between lines the computer spits out typing sounds and a virtual agent saying please hold on while I look into that.

Of course a better fix would be a combination of the two. Have some agent read your original email sent through some secure internal site and build and classify a case in the system with email attached and then reply to let you know there is a secure reply with a chat link to the complete case detail with time frames reserved for high responsiveness.