Nice!
In terms of making the algorithm a bit more human-like, some time ago I wrote some Excel-based code to help me with difficult sudokus, without just solving it for me. The two bits of logic were:
1) A bit that filled in every cell, showing every number it could be (so it could have multiple values)
2) A filter that, for each number, coloured all the cells based on whether they were definitely that number, might be that number, or definitely weren’t that number. This allowed me to spot the patterns that step 1 couldn’t solve. I reckon you could get this pattern spotting into code.

I wanted to avoid trial and error, since I believe that most sudokus can be done without it.