There has certainly been a leaning towards ex-military pilots by most ASU's because much military experience (Low level, night, map-reading, surveillance etc) is relevant to Police work.
I will stick my head above the parapet and say that the more North Sea offshore experience you have the less likely you are to be employable in demanding roles onshore. Its a whole different world..you are on your own mostly, with little back-up. That does not mean I don't respect the offshore guys... I have done it, both NS and South China Sea..its just different.
Don't know about EMS - it certainly has its own stresses but since its usually daylight only, that does ease the burden on your skills.
A small point - I don't think Police work pays particularly well either compared to present NS deals.