I'm afraid that's rather unavoidable with scatters. To completely prevent intersections you would need to use a physics simulation which Forest Pack does not employ because the plugin is highly optimised for speed, and a simulations are just too slow for scattering over a large area.
That said, the individual circular patches used by the presets were created using physics, but as we can see from your screen shots, it's where the patches overlap that they intersect. This is difficult to avoid while maintaining a contiguous surface.
If the ground is flat, one option to minimise intersections could be to make square patches designed to tiles in all directions, then use a Full distribution pattern to lock them together like a jigsaw. Repetition might be more visible, but it could be disguised by randomising materials using Forest Colour and rotating the patches in 90 degree increments.
If the camera is very close you could also try mixing a physics simulation for the foreground with a patch based approach further from the camera. This may even be easier in the future because, though it's not available yet, Forest Pack 6 will support scattering using particles.
I'm sorry I can't give you an easy solution for this one, but I hope that helps a bit. Please let me know if you have any further questions.
All the best,