Completed Word Grid
Definitions of the wild words, for the curious
Completed Score Grid
I really wanted to try and solve this as manually as I could, but seeing how many possibilities there were after my first attempt (2997 for one row!), I soon realized this was almost impossible, so I fully automated (brute-forced) this solution.
First, the basic deductions from extending regions:
Next, look at some sum cages.
Next, the upper left:
...And from here, I believe there are multiple solutions.
Unless I've made a mistake (which very well could be the case), this demonstrates at least two solutions to the puzzle. (I've highlighted 1s, 2s, and 3s for easier checking.)
Statue Park clues all give the same amount of information: there is a tile here/there is not a tile here.
But depending on their location, you can get a different amount of information! To demonstrate this, consider this puzzle (where the piece bank is the pentominoes). Say I've already determined the two shapes I've shaded in.
If I want to place a clue at ...
We can try the following
I have also noticed that
Hence, we have two valid and different solutions motivated by different aspects of the letters.
Here is the official solution from my puzzle book.
Sorry for the confusion. Because there is only one solution printed I thought the solution is unique. Now I saw that this was missleading.
And I can't see any further restrictions in the solution.
@all Thanks for your help :)