A fair bit of emphasis seems to have been attracted by the medical/fitness aspect.
If you are working for a civilian company, albeit contracted to the military, surely a JAA class1 suffices. Surely the whole point of civilian contracting to the military is to minimize admin, costs and military imposed constraints.
I think difficulty will arise in contractual terms. If there is a waiver where a contract of employment can be replaced at the behest of a Queen then there simply isn't any point in a contract at the first instance.
This gig, and little seems to be known about it, would have to attract large cash for A330 p1s nevermind the right ones amongst them.