Changing AuthorizedKeysFile in `sshd_config` not solving public key auth failure with encrypted home

The case sounds simple. I have my home folder encrypted using eCryptFS on the "server", it looks like:

/home/<user_name>/.Private on /home/<user_name> type ecryptfs (ecryptfs_check_dev_ruid,
ecryptfs_cipher=aes,ecryptfs_key_bytes=16,ecryptfs_unlink_sigs,ecryptfs_sig=<...>,
ecryptfs_fnek_sig=<...>)

Because the "authorized_keys" file is in ~/.ssh by default, which is not decrypted before I actually login, I moved that file to /home/ssh/<user_name>/authorized_keys. The permissions of /home/ssh/<user_name> is 755, and that of the authorized_keys file is 644. The file contains the public key of the machine that I would like to login from.

Then I changed the "AuthorizedKeysFile" option in /etc/ssh/sshd_config, to /home/ssh/%u/authorized_keys. As is suggested by this manual: https://help.ubuntu.com/community/SSH/OpenSSH/Keys and this post: https://stephen.rees-carter.net/thought/encrypted-home-directories-ssh-key-authentication. I searched for this problem here but mostly got the same instructions. However, still I cannot log-in without a password.

Then I did some tests, I generated a pair of SSH keys on the server (which I would like to SSH into), and copied the public key to /home/ssh/<user_name>/authorized_keys. Then I found that I cannot even login to localhost without using my password, on that server machine. Therefore, I assume that for some reason SSH daemon didn't load the authorized_keys file at all. I also tried to put the file in the original location which is ~/.ssh, still cannot do public key auth.

Attached is my sshd_config:

# Package generated configuration file
# See the sshd_config(5) manpage for details

# What ports, IPs and protocols we listen for
Port 22
# Use these options to restrict which interfaces/protocols sshd will bind to
#ListenAddress ::
#ListenAddress 0.0.0.0
Protocol 2
# HostKeys for protocol version 2
HostKey /etc/ssh/ssh_host_rsa_key
HostKey /etc/ssh/ssh_host_dsa_key
HostKey /etc/ssh/ssh_host_ecdsa_key
HostKey /etc/ssh/ssh_host_ed25519_key
#Privilege Separation is turned on for security
UsePrivilegeSeparation yes

# Lifetime and size of ephemeral version 1 server key
KeyRegenerationInterval 3600
ServerKeyBits 1024

# Logging
SyslogFacility AUTH
LogLevel INFO

# Authentication:
LoginGraceTime 120
PermitRootLogin without-password
StrictModes yes

RSAAuthentication yes
PubkeyAuthentication yes
AuthorizedKeysFile  /home/ssh/%u/authorized_keys

# Don't read the user's ~/.rhosts and ~/.shosts files
IgnoreRhosts yes
# For this to work you will also need host keys in /etc/ssh_known_hosts
RhostsRSAAuthentication no
# similar for protocol version 2
HostbasedAuthentication no
# Uncomment if you don't trust ~/.ssh/known_hosts for RhostsRSAAuthentication
#IgnoreUserKnownHosts yes

# To enable empty passwords, change to yes (NOT RECOMMENDED)
PermitEmptyPasswords no

# Change to yes to enable challenge-response passwords (beware issues with
# some PAM modules and threads)
ChallengeResponseAuthentication no

# Change to no to disable tunnelled clear text passwords
#PasswordAuthentication yes

# Kerberos options
#KerberosAuthentication no
#KerberosGetAFSToken no
#KerberosOrLocalPasswd yes
#KerberosTicketCleanup yes

# GSSAPI options
#GSSAPIAuthentication no
#GSSAPICleanupCredentials yes

X11Forwarding yes
X11DisplayOffset 10
PrintMotd no
PrintLastLog yes
TCPKeepAlive yes
#UseLogin no

#MaxStartups 10:30:60
#Banner /etc/issue.net

# Allow client to pass locale environment variables
AcceptEnv LANG LC_*

Subsystem sftp /usr/lib/openssh/sftp-server

# Set this to 'yes' to enable PAM authentication, account processing,
# and session processing. If this is enabled, PAM authentication will
# be allowed through the ChallengeResponseAuthentication and
# PasswordAuthentication.  Depending on your PAM configuration,
# PAM authentication via ChallengeResponseAuthentication may bypass
# the setting of "PermitRootLogin without-password".
# If you just want the PAM account and session checks to run without
# PAM authentication, then enable this but set PasswordAuthentication
# and ChallengeResponseAuthentication to 'no'.
UsePAM yes

The authorized_keys file is located here:

$ ll
total 24K
drwx------  2 root        root         16K Feb 26 19:23 lost+found
drwxrwxr-x  3 root        root        4.0K Mar  1 13:12 ssh
drwx------ 22 <user_name> <user_name> 4.0K Mar  1 13:42 <user_name>
$ cd ssh
$ ll
total 4.0K
drwxr-xr-x 2 <user_name> <user_name> 4.0K Mar  1 13:12 <user_name>
$ cd <user_name>
$ ll
total 4.0K
-rw-r--r-- 1 <user_name> <user_name> 790 Mar  1 13:32 authorized_keys
$

I also tried to change permissions (of the directory and the file) to 700 and 600, didn't work either...