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.