Partial answer

Chapter One grid

After the edit, this grid satisfies the constraints:

M C H E W L I
A R T S H A C
E H E T I R E

I don't know whether this is the only solution or not, but this was my general thought process:

Assuming that there aren't any extraneous letters, MARCH must start in the top-left corner, since it is the only word with an M in it.
If we then assume that there is only one S in the grid, then both HEARTS and CHESHIRE must pass through the centre square. Noticing that both these words share a bigram with MARCH (AR and CH respectively), we can fit letters in the grid assuming that these bigrams are indeed shared letters in the grid paths, leading to the left part of the grid being
M C H E . . .
A R T S . . .
E H . . . . E
Then, noticing that the latter half of CHESHIRE differs from HARE by only one letter, and assuming the H and RE are shared between them, and keeping in mind the remaining words, the grid fills itself in.

Chapter Two words

The words are:

CHARM, TEETH, REACH, and LEWIS, leaving the I on the bottom row left out. Now where might I have heard that name before?

Here's a visual:

Sidenote: Chapter One in its previous form could be solved using only 19 letters, in the following way:

M A E H W . .
C R T I R E C
H E S H A L I
(additionally, the ALICE could start in the top-right corner and go clockwise for an alternative 20-letter solution)

Partial answer

Chapter One grid

After the edit, this grid satisfies the constraints:

M C H E W L I
A R T S H A C
E H E T I R E

I don't know whether this is the only solution or not, but this was my general thought process:

Assuming that there aren't any extraneous letters, MARCH must start in the top-left corner, since it is the only word with an M in it.
If we then assume that there is only one S in the grid, then both HEARTS and CHESHIRE must pass through the centre square. Noticing that both these words share a bigram with MARCH (AR and CH respectively), we can fit letters in the grid assuming that these bigrams are indeed shared letters in the grid paths, leading to the left part of the grid being
M C H E . . .
A R T S . . .
E H . . . . E
Then, noticing that the latter half of CHESHIRE differs from HARE by only one letter, and assuming the H and RE are shared between them, and keeping in mind the remaining words, the grid fills itself in.

Chapter Two words

A possibility for the words are:

CHARM, TEETH, REACH, and LEWIS, leaving the I on the bottom row left out. Now where might I have heard that name before?

Here's a visual:

However this partitioning doesn't work for Chapter Three...

Sidenote: Chapter One in its previous form could be solved using only 19 letters, in the following way:

M A E H W . .
C R T I R E C
H E S H A L I
(additionally, the ALICE could start in the top-right corner and go clockwise for an alternative 20-letter solution)

Partial answer

Chapter One grid

After the edit, this grid satisfies the constraints:

M C H E W L I
A R T S H A C
E H E T I R E

I don't know whether this is the only solution or not, but this was my general thought process:

Assuming that there aren't any extraneous letters, MARCH must start in the top-left corner, since it is the only word with an M in it.
If we then assume that there is only one S in the grid, then both HEARTS and CHESHIRE must pass through the centre square. Noticing that both these words share a bigram with MARCH (AR and CH respectively), we can fit letters in the grid assuming that these bigrams are indeed shared letters in the grid paths, leading to the left part of the grid being
M C H E . . .
A R T S . . .
E H . . . . E
Then, noticing that the latter half of CHESHIRE differs from HARE by only one letter, and assuming the H and RE are shared between them, and keeping in mind the remaining words, the grid fills itself in.

Chapter Two words

The words are:

CHARM, TEETH, REACH, and LEWIS, leaving the I on the bottom row left out. Now where might I have heard that name before?

Sidenote: Chapter One in its previous form could be solved using only 19 letters, in the following way:

M A E H W . .
C R T I R E C
H E S H A L I
(additionally, the ALICE could start in the top-right corner and go clockwise for an alternative 20-letter solution)

Partial answer

Chapter One grid

After the edit, this grid satisfies the constraints:

M C H E W L I
A R T S H A C
E H E T I R E

I don't know whether this is the only solution or not, but this was my general thought process:

Assuming that there aren't any extraneous letters, MARCH must start in the top-left corner, since it is the only word with an M in it.
If we then assume that there is only one S in the grid, then both HEARTS and CHESHIRE must pass through the centre square. Noticing that both these words share a bigram with MARCH (AR and CH respectively), we can fit letters in the grid assuming that these bigrams are indeed shared letters in the grid paths, leading to the left part of the grid being
M C H E . . .
A R T S . . .
E H . . . . E
Then, noticing that the latter half of CHESHIRE differs from HARE by only one letter, and assuming the H and RE are shared between them, and keeping in mind the remaining words, the grid fills itself in.

Chapter Two words

The words are:

CHARM, TEETH, REACH, and LEWIS, leaving the I on the bottom row left out. Now where might I have heard that name before?

Here's a visual:

Sidenote: Chapter One in its previous form could be solved using only 19 letters, in the following way:

M A E H W . .
C R T I R E C
H E S H A L I
(additionally, the ALICE could start in the top-right corner and go clockwise for an alternative 20-letter solution)