Here’s another idea for a possible clue-giving system. After each turn the fugitive reveals the shape of their stones relative to each other. In other words, take the actual game position, delete all detective stones and star-point markings on the board as well as the edge of the board and the grid is extended, so the detectives don’t know where exactly on the board is this shape.
For example, after the first move the shape is always …
After the second fugitive move, it may look as follows
Note that the detectives don’t know which of these was played first. After even more moves the shape may look like this:
This gives the detectives a strong hint, so finding a balanced game between X detectives on a board of size Y will be a challenge again.
I realised there is an unintentional side-effect, namely the fugitive can’t really play shapes that are far apart. In the extreme case where the fugitive plays two corner points diagonal to each other, the detectives could deduce exactly where the stones are. Even if we take away the star points and the edge of the following board …
… the corner points are the only intersection wich are 18 diagonal steps apart from each other, and so the detectives would get full information.
Similarly, if the stones are not quite as extreme but still far apart, the number of possibilities is low.
In order to mitigate this effect, perhaps we could change the clue slightly. That is by taking the board (withhout detective stones, of course), erasing all borders and star-points, and the fugitive may apply a toroidal translation to the board. So in the above example, the two corner points can then be shown as a kosumi-shape:
Of course the detectives know that the shown shape is subject to toroidal translation. This way the number of possibilities should hopefully be independent on how far apart the fugitive plays.
One downside is that its kind of complicated.