Fill in the following crossword, such that each box has a letter filled in it by its across clue which is either directly after or before the letter filled in it by its down clue in the alphabet. Note that A is considered to “wrap around” to Z. I’ve given the grid twice, for convenience.
Now I know that I already said that I wanted to push the boundaries of Knapp Daneben, but I really doubt anyone expected a crossword as even a possibility to appear in this theme! I’m not generally a great crossword constructor, but I’d think it would be interesting to see other crosswords with the Extra Grid or Toroidal variations, for example. (Maybe even Exactly One Letter somehow?!)

ACROSS
1.) One who does jack
6.) Church songs
7.) Chose
8.) Without fallacy
9.) Babble on
DOWN
1.) “_____ be square” (2 wds.)
2.) The parts of DNA which get converted into proteins
3.) Someone clumsy
4.) Extinct birds
5.) Mount for a lancer