Not directly related to your initial question, but, you might consider reversing the itinerary
and going to Edinburgh first, then to Amsterdam, and then back to the US.
The fares out of Edinburgh back to the US are likely to be higher, both from supply/demand
and from the UK departure taxes. The taxes are high %-wise for the flight to Amsterdam, but it's
a much cheaper and shorter flight.
You also have a better chance of the more efficient non-stop or connection path if you fly
back from Amsterdam.
I flew into London (easy, obviously) and then took the train up to Edinburgh; that's another
option.