Hi, Jenn’
You just need to solve some of the down clues and it becomes really clear which solutions go where because the crossing letters leave you in no doubt.
BB, funnily enough I was thinking of the same puzzle with the two grids. I think it was Twin but I may be wrong.
I also recall a puzzle by Boatman which appeared just prior to the Brexit result, where depending on your interpretation of the clues to grid revealed either ‘leave’ or ‘remain’, or something like that.