Let's say I have a puzzle like this:
The idea is that since you're on ice, once you start moving you can't stop until you hit a rock. If you treat the red/blue patches as paint that leaves trails when you move, then trying to collect all the coins in the fewest number of moves spells out a word.
However, as you can see, this puzzle heavily restricts what moves you can perform, making it very easy. I'd like to construct a puzzle which gives more freedom and possibly involves crossing over the same paint patches multiple times, but I'm afraid that the resulting puzzle might have multiple solutions or the painted word might be unrecognisable if you do things in a different order.
So my question is this: Is there a good way of either 1) generating a more open puzzle which still guarantees a unique solution or 2) modifying the puzzle mechanics so that 1) is easier to do?.
Edit: To clarify I'm not asking about generating these sorts of puzzles in general. Instead, given a target word, how can we generate a unique-solution puzzle which spells out that word? (via paint/any other mechanic)