Bridge the gap
There is an almighty gap between management and technical staff. In large companies the rift can be so big that the two camps have little in the way of communication, no trust or even a basic understanding of what the other guys do.
That's where you come in. As someone with a foot on either side of the divide, you can act as a translator between tech-speak and management-speak, arbitrate technical requirements that are clearly impractical, explain management strategies that appear nonsensical and be each side's "trusted friend and ally" in the common battle to get stuff done.
One day you might be explaining in business terms to the CIO why he/she/it needs to spend £100k on a new storage array and the next you could be telling the developers why their pet project is doomed to fail and they need to focus on testing the new products instead.
The big problem is that most companies have their heads inserted so far ... , that they can't recognise the need for such a person as yourself. Both sides are firmly convinced that they are right, if only "those idiots could see what we are doing" and neither side has any respect for the other's point of view. You need an "in" which would probably only come from a (social) networking contact, rather than through an agency - which would be blind to this sort of role. You also need a direct (if "dotted") line to a C-level person, so I suggest you take up golf, too.
As for a job title: Recto-Cranial Removal Specialist might work.