Hi Eli, sorry for the really slow response - we've been a bit bad at checking this group!
Unfortunately crossword grid data isn't currently available in the public Content API. The reason is that we still give prizes for a couple of crosswords and the API response includes the solutions as well as the clues. Clearly we could work round this by just opening up access to crosswords that are over 2 weeks old, but we don't have the capability to do that at the moment.
Sorry this is such a rubbish slow answer. If you're still looking to do stuff with crosswords let me know, I might be able to sort you out a temporary key to access them.
Thanks
Phil