I've flown south four almost 30,000 blocks now, and I haven't had any luck. The player dot's in the top right corner, meaning that it IS in the direction I'm going in (I hope). Am I going the wrong way somehow?
That is the right direction, at least partially, you might be better off going southwest until the dot starts moving along one of the edges.
Woodland mansions are quite rare so you may well have to go further than 30,000 blocks.
The Wiki says:
"Woodland mansions generate very rarely in Dark Forests and their Hills variants, often appearing tens of thousands of blocks away from the spawn."
and also claims that the mansion shown on an explorer map wouldn't necessarily be the closest one.
I've since found the mansion. Quite underwhelmed by it, but at least I got those totems.