A hierarchical strategy for solving Wilson grid problem in Lp norms with p finite: Slice up the plane using a square grid of side L. Within each grid square, use the best G1-G2 matching. The result will leave unmatched, up to N points per square, where N>0 if the number of points of G1 in that square is unequal to the number of G2 points, and N=O(L) is easy to see. Now, erase all the matched points from consideration. Do it again using grid of side sqrt(L) times larger. Keep going in this way. Intuitively speaking each stage in this process gets rid of all but a fraction O(1/L) of the unmatched points, and increases the length scale by factor sqrt(L). Therefore, in any Lp norm, the total cost of the matching it produces, should be finite per point (geometric series converges). This suggests that in any Lp norm with p finite, Wilson's problem has a solution with finite c. This however does not solve the p=infinity case he wanted, and there will be arbitrarily far-separated mates produced (they just are rare). Actually, I think this "suggestion" could actually be turned into a "proof" because the grids at each stage can be randomly translated, and then the unmatched points counting bound will necessarily hold in expectation at each stage, and hence there must exist translations which do better than expectation, and hence there must exist suitable scaled and translated grids that make this argument work. I have not worked thru the details of that, though.