All I can do is repeat that getting the train from the Newcastle area to LHR is not remotely arduous in my experience.
The only problem is the return arrival time of likely airlines is just about too late to be confident of any transport back home.
From AMS you have the choice of KLM, CI and probably others and book at the right time and you can get a very reasonable business class fare (otherwise KLM charge about £600 for the short hop to AMS, greedy sids)