Each puzzle page has a sword on the bottom that matches the length of the puzzle's answer and also singles out a letter from the answer. Ordered by puzzle number, these answers and letters are:
canCel fenCe staRes incRement whoOps turnOver chaSte denSity wiSe induStry joUst outpUt anSwer viSually
There are a few observations that can be made at this point:
1. The swords are paired, so that puzzles 001 and 002 have the same sword, puzzles 003 and 004 have the same sword, and so on.
2. All of the odd-numbered puzzles have a sword passing through the header from top-left to bottom-right, and all the even-numbered puzzles have a sword from top-right to bottom-left.
3. The singled-out letters in each pair of swords are identical and spell out CROSS US.
This suggests that we should cross the swords so that they intersect at the common letter. For CANCEL and FENCE, it would look something like
C F A E N N C E E L
If we exchange the parts below the crossing, we can read CANCE and FENCEL. The key here is to realize that the C can be replaced in each of these to get the words CANOE and FENNEL. Doing the same thing for each pair of words, we get:
canCel + fenCe -> canCe + fenCel -> canOe + fenNel staRes + incRement -> staRement + incRes -> staTement + incHes whoOps + turnOver -> whoOver + turnOps -> whoEver + turnIps chaSte + denSity -> chaSity + denSte -> chaRity + denOte wiSe + induStry -> wiStry + induSe -> wiNtry + induCe joUst + outpUt -> joUt + outpUst -> joLt + outpOst anSwer + viSually -> anSually + viSwer -> anNually + viEwer
The new letters spell out Layton's location, ON THE IRON CLONE (a reference to a phrase from Game of Thrones).