"Did the previous Head of Engineering not make the move to Turweston?"
There was no such post at Shoreham. The Director of Engineering was appointed so to allow the Chief Engineer and Deputy Chief Engineer to concentrate upon their day jobs, ie approving aircraft and mods for flight.
The Dir of Engineering has a broader role and it encompasses such things as governance, CAA liason and liason with the plethora of associated bodies and parties that were preventing the CE and DCE from turning around work packages with the speed that was desired of them.
Hope that this helps,
Stik