Actually, one of the interesting things about cryptic crosswords is that, in some ways, the rules are far more codified.
The specifics definitely depend on the paper, of course, but basics like the fact that the majority of the clues are actually two halves, clueing the word two different ways, and that anagrams are always explicitly clues using words such as "scrambled," "drunken," "off" or whatever could actually make it easier for the human to guide the ML.
well yes, but the beautiful thing about UK cryptics at least is that they regularly intentionally misdirect the user, so you spend some time going down a rabbit hole and realise that you're on a hiding to nothing. I think that kind of game play is what makes a rules-based approach more challenging. I'll have to check out Crossword Genius though.
That might make it easier, not harder, for computers.
Adding in multiple distractor possibilities is a good way to make things harder for humans, with our limited working memory & difficulty chasing a lot of possibilities in parallel, but for a computer that's borderline trivial while it's evaluating each candidate accurately that's hard for a computer to get right. (Think of chess or Go where a computer can descend the game tree down millions of paths easily, but it's accurately evaluating a single board position which is extremely difficult; human players, on the other hand, can evaluate a board at a glance, but can only think through a few lines of play at a time.)
If the rules are simple but there's multiple candidate, the AI will just split at each possible candidate and pursue them until the AI can check whether it fits in the crossword grid or not.