I agree the bridging the taxiway seems highly unlikely which means going underneath is the only option unless the plan is to stop the rail link short of the taxiway in which case you'd still need some kind of shuttle bus to the terminal which seems a bit pointless since that's what they're trying to replace.
I can only see the only realistic option being tunneling - either reducing capacity of the existing one to allow a rail link in alongside (as was I believe the original plan) or creating a new tunnel space