You're taking the wrong approach. You want to generate chess, problems, it seems, and your approach, while valid, won't yeld useful results due primarily to two reasons:
1 - for a given soluction it'll generate hundreds or thousands of possible starting positions
2 - a chess problem (what you call the original board position) has many subjective qualities, such as beauty, difficulty and likelihood to occur in a regular game.
If you can develop an algorithm to evaluate a chess problem according to the criterions in #2, you can use that to filter out the hundreds of positions generated in step #1. But would it be worth your while? It might be cheaper to get a good chess player to invent problems for your.
ESC[78;89;13p ESC[110;121;13p
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