could a option be added to the backgrounds options to switch to a default background that is set for each puzzle. that would use what you feel is the best background for that particular puzzle. possibly have this option not override whatever the user currently has selected within the save file. that way they can just switch to the one they like, if that one doesn't work for them. and possibly toggle between the two to see which one works best for them. even if they had to go back and forth between the puzzle screen and the options menu, i still think many would enjoy this greatly

plus this would open up your options for stuff to do in each puzzle as well. we've really been enjoying your Easter Eggs that some puzzles have on completion