https://lichess.org/@/Tobs40/blog/there-is-no-reachable-ches... describes how the author removed some more complicated rules in the first pass, and is willing to re-introduce them, if necessary. Ie if the solution found violates them.

Interestingly, mixed integer linear programming solvers already support these. The technical term for this is 'row generation'. It comes from the usually way these problems are written in matrix form, where rows correspond to constraints and columns correspond to variables.

(Dynamically) adding a row is equivalent to introducing a constraint only if it's violated.

This approach is often used for the traveling salesman problem.

(Weirdly enough, Wikipedia has https://en.wikipedia.org/wiki/Column_generation but nothing on row generation.)