How to reason through larger boards without relying on random trial and error.
Hard Shikaku puzzles usually stop being about obvious forced placements and start being about candidate management. The board is still logical, but you need to compare possible rectangles instead of only looking for immediate fits.
For each clue, list the rectangle dimensions that match its area. A 12 can be 1x12, 2x6, 3x4, 4x3, 6x2, or 12x1, but board edges and neighboring clues eliminate many of those.
If every valid candidate for a clue covers the same cell, that cell is effectively claimed. You can use that claimed cell to eliminate candidates from other clues that would overlap it.
Sometimes a candidate seems valid by itself but blocks every possible placement for a neighbor. That candidate cannot be part of the solution. This is one of the most common hard-puzzle deductions.
When solved rectangles create a bounded region, compare the number of open cells with the sum of clues that must live inside the region. If the numbers match, no clue inside may extend outside and no outside clue may enter.
Avoid shallow guessing: Trying a rectangle is useful only if you follow its consequences. If it creates an impossible cell or leaves a clue with no candidates, undo and eliminate that candidate.