Mooncow,
Your post prompted me to stop cold-solving (17 fairly confident answers in) and start staring at the grid, and I’m glad I’ve done so because I’m now suspecting there’s something fundamental I don’t understand about this puzzle, or maybe something blindingly obvious I’m missing about crossword grids in general.
Simply looking at the Down answers, they appear to require more columns than are present in the grid, which is a shock. By which I mean, two answers containing more than 12 cells between them presumably cannot occupy the same column, and on that basis, there appear to be more than 12 columns’ worth of answers.
I have no idea if I’ve stumbled upon an observation that’s key to cracking the puzzle, or (as I fear) one that simply illustrates my idiocy!