Mm, yeah, I've tried to work out things based on the symmetry, but I'm still not *quite* seeing it... So c2r9 + c1r10 are the "correct" solutions there, but what would prevent the solution from being c1r9 + c2r10 instead? That would satisfy the symmetry and complete the first two columns + last two rows.

Or, still keeping with the symmetry but not doing a solution which helps fill r5/c6 completely, this selection would "solve" the same rows, yeah? c1r5 + c2r8 + c3r9 + c6r10...

I feel like there's just some intuitive leap I'm not making here -- having trouble adapting the left-right symmetry stuff present in earlier puzzles to this diagonal-fold version instead...

I've stared at this for a few and can't find anything else that would deem worth of X or [] based on standard filling. The major hint is the symmetrical hint of Top-Down matching Right-Left. Based on the symmetry rules w/i the game, Column Two Row 9 would be a []. The 1:1 meeting the 1:1 symmetrically. That will go the same with Column One Row 10. This then fills Rows 9/10 and Columns 1/2 with X's. You're able to fill row 5 fully and Column 6. Due to the X's the 3:1 columns/rows of 4 and 6 can be filled. And the rest of the map.

So you're right, the basic fill rules wouldn't apply but the symmetry rules would get you out of the jam