Well, I hesitated to answer at first since my info is not from first hand experience, but maybe I can still help.

The MRT runs about 6am-12am. So for a 6am flight, the MRT is not an option. Taxis from the city cost no more than US$15, which includes a slight surcharge that is assessed after-hours.

Unfortunately, you can't get to the transit hotel without a boarding pass. And since UA and NW check-in counters don't open until about 3:30a or 4am, you won't be able to get a boarding pass the night before your flight.

However, if you want to visit the airport 24 hours before your flight, you can check-in and get a boarding pass the morning before your departure. The rule is is that you can check in starting at 24 hours before your flight.

Or, a less than ethical option would be to purchase a fully refundable ticket from an airline whose check-in counter is open when you get there, and then cancelling it after you pass security....