One possibility for an early morning SIN arrival might be to consider a transit hotel room in the Changi terminal for a few hours to shower and rest until you can get to your hotel at their earliest permitted check-in. Only snag would be how the airline would handle your checked bags when you don't arrive at the luggage claim at the expected time. And, for UA in particular, If you show up later, are there even UA personnel available after ~1000am to get your bags?