I'm possibly being a bit thick, but what is there against the airport providing a subsidy to National Express or another coach company for early morning / late night ? It solves all the problems of rail engineering works, and means rather than one single train service with 300+ seats (and potentially a very long wait between services) you can instead have coaches spaced at regular intervals. Maybe set up some revenue sharing scheme so coach and train have interchangeable tickets. If these coaches can show up in the national rail timetable this would encourage potential passengers
Stansted had far more pax per year than Southend does before early morning / late night trains were introduced. I really think that some sort of interim and lower cost scheme is needed to ensure demand can be proven further to all the relevant stakeholders in a train service