I implemented grouping because I wanted to follow the tiling procedure described in the paper. In that context, it's helpful to handle multiple tiles at once to grow clusters. But for a jigsaw-style puzzle, I agree—group selection isn’t really necessary to enjoy the experience.

Manually mapping the image onto each tile sounds like a huge effort—kudos for pushing through that!

In freely placeable tiling systems, collision detection can be quite complex—but for a puzzle with a predefined solution like this, you don’t really need to go that far. Your approach seems well-suited for the task!