I tend to fly mid afternoon (approx 14:00) if I can (seems to be the cheapest price at about £88 for EDI-AMS return). All the times I've flown that route where there has been a Europe Select part I’ve been upgraded
I tend to book 2 or 3C and on the phone they say they can't guarantee the seat, but in check in they just give me an ES boarding pass. I'm only GE, but my dad PE has been upgraded all the time on this route as well.
I've only ever seen ES on the 737s with EDI-AMS
Chris