Klondike Returns

Since 90s from college I read the old article of Martin Gardner from Scientific American.
This problem probably has been one of the most famous I have seen through the years, it appears with its own frequency.

With the original problem there are hundreds of solutions, some of them are

1. W W W E SW E NW SW NE NE NE SW SW SW NW
2. NW SE W SE SE W NW SW NE NE NE SW SW SW NW
3. N W E SW S E NW SW NE NE NE SW SW SW SE
4. NE W S SW S E NW SW NE NE NE SW SW SW SE
5. E W S SE S NW NW SW NE NE NE SW SW SW NW
6. SE W NW SE W W NW SW NE NE NE SW SW SW NW
7. S W E SW W NW SW NE NE NE SW SW SW NW


And with the troublesome fixed there are only two solutions:

SW SW NE NE NE SW SW SW NW
SW SW NE NE NE SW SW SW SE


I made Yet Another Search Program for it. where the troublesome 2 from Gardner article is verified, but I found a if we change (besides of the 2 mentioned) number 4 at (x,y) then there will be only one solution.

But there is a new probable modification I found to make the puzzle with an unique solution, which would be