This isn't any different if you're flying other airlines. They either have extremely limited saver space (AA) or have dynamic pricing that makes most premium cabin award space ridiculously expensive (DL).

With that said, you've just got to look around. I've found FI premium space (direct) at the edge of the current window, QX first space (on multiple routes from LAX) around the first of this year and I was successful in booking both CX F and J space next summer with a JL J space for the return trip. I also found some DE space around the time of Oktoberfest. So options are out there.

Believe it or not but I think the hardest space to find is AS' own saver space for positioning flights to partner gateway cities. It's so bad I actually booked AA space to ORD to position my CX award (yes, sometimes you have to make sacrifices, but that's the game now - the scheduling worked out better on AA anyway, and they had saver space available so it was worth it to ignore the hassle).

I'm sure it'll take a long time to get SQ and EI space available for redemptions, if only because their IT and systems are absolutely archaic. But by then, you'll have hoarded so many miles it won't have mattered!