OK so we have discovered the terminal is 42 metres higher than the railway line.
A quick look on Google reveals this little gem
On the Docklands Light Railway the entrance to the tunnel from the original London and Blackwall railway viaduct to the tunnel to Bank has the steepest gradient on any British railway at 1 in 17 (5.88%).
Say the station is a mile from the terminal this would make it 5,280ft away, add 5.88% and that would add 310ft or 94metres. So a docklands light railway type train could get the the terminal.
Back to the question do you go over or under taxiway Alpha?
Also there is another question. If the airport can attract 12.3million passengers without a link and probably over 13 million next year with more to follow. What value does an expensive to build link give the airport unless they are looking at life beyond 18 million?