I implemented a plain vanilla backtrack and it worked for both (the only little consideration is not to test all lines/columns/boxes, only that one that has the last changed cell.)
There might be “anti-backtrack” challenges (no or rare hints on the upper part of the grid or first empty cells tending to be 9 8 7, meaning the algorithm cannot prune early), but none of the test cases/validators seem to be of this kind, or the machine is now fast enough no matter what is the input.