Decode the cipher in Ink Cipher!

Ink Cipher is a sleek take on the puzzle sometimes known as the Cipher Crossword, Code Word, Code Breaker or Kaidoku.

You're presented with a grid filled with words... except all the letters have been replaced by numbers. Each number represents its own letter. Using your knowledge of the English lexicon (and the occasional hint from the puzzle title), fill in the letters where you can recognize words, and crack the cipher!