Welcome to FT!
EK inventory management releases seats fairly close to the departure date. Your best bet is to set up an alert on expertflyer for 'N' inventory. Alternatively, consider booking a paid ticket and upgrading segments with miles if you can fly separately from your friends.
I wouldn't say you should get your hopes too high as that's also peak period at the end of June. Keep a look out for SQ award seats too, as they're much easier to come by! Good luck!