I'm a little confused by your post. Did you open-date your ticket? Why would you book an itinerary if you couldn't get the flights you wanted? You booked it with UA in what class if theres no availability?

1. I see availability in Y for July 10th on EK386. Trying waitlisting for First and Business.
2. Try flying DXB-SIN and buying the last portion on a cheap LCC.
3. Try flying DXB-KUL and buying the last portion on a cheap LCC.

2+3 may require re-route fee.