While I was discovering the solution noted above (15b), it occurred to me that there are are some intrinsic limits on grid templates, which limit the types that need be considered.
For example, a template with 2 runs of length 9 that are aligned and adjacent can never
deliver a unique solution.
That's because swappping the row or column values must inevitably deliver the same sums.
Other limits seem to be less obvious, but my experiments, plus a canvas of various puzzles I could find to test, all seem to point to the following limits on what I call critical blocks
, which are rectangles of contiguous blank cells:
Any block of blank cells that exceed these limits (such as 5 x 5) is almost certainly incapable of delivering a puzzle with a unique solution.
So I was lucky with the 15x15 case because the 5x5 corners (on which I was building my solution) have 2 hint cells, so pass this test.
Most of the other large sample grids I generated are clearly useless, and I will probably have to revise my table quite significantly.