The New York Times Hard level sudoku game is at this link: www.nytimes.com/puzzles/sudok... I used the solver on the sudokuexchange.com website to play this game.
It was a trick one today. It took me almost half an hour, and while I used some notation, I managed to limit that to some pairs, a triple and some bi-value. If notate fully, I find it confusing.
You got it so well with the 18 pair in block 2. Unfortunately, you staid in your microcosm of what this meant in block 2. You have to look at the grid. The 1s are now confined to the middle and right in block 2. Same situation for the 1s in block 5. Only one place left for the 1 in column 4: row 9. This now means the 2 in row 9 is confined to col 5. The puzzle can now be finished by a beginner.