First I tried two of the most popular Android apps for sharing files over WiFi FTP server and WiFi FTP Server:
Both worked great with Nautilus. Except neither one relayed "Last Access Date" to Nautilus like my projected needed. Both showed "Unknown" instead of a valid date.
As mentioned in other answer
curlftpfs doesn't work so I tried:
sudo apt-get install sshfs
However neither of the Android WiFi file sharing apps would let me signon. An email to tech support confirmed they don't support Secure Shell, only FTP which is notoriously insecure.
No matter which app you use you need to create a directory to mount the remote folder in. I used:
chown rick:rick /mnt/phone
"rick" being the User ID.
You will want to sign onto your router and make the IP address (in my case 192.168.0.11) static so it doesn't change each time your phone connects to your router. Here is a link to give you an idea but, yours will no doubt be different:
Since FTP Servers on Android don't support SSH the next step try SimpleSSH as recommended here:
However SimpleSSH doesn't seem recommended in Google Play Store that well? Use this instead with very high ratings SSH/SFTP Server - Terminal from Banana Studio:
During testing and crashes you'll need to unmount your drive:
$fusermount -u /mnt/phone
After installing SSH/SFTP Server - Terminal use this command:
$ echo rick | sshfs -o password_stdin -p 2222 email@example.com:/ /mnt/phone
$ cd "/mnt/phone/Music/Uriah Heep/The Magician's Birthday"
rick@alien:/mnt/phone/Music/Uriah Heep/The Magician's Birthday$ ll
-rw-rw-rw- 1 root root 8204186 Mar 10 2016 01 Sunrise.m4a
-rw-rw-rw- 1 root root 5375331 Mar 10 2016 02 Spider Woman.m4a
-rw-rw-rw- 1 root root 7599684 Mar 10 2016 03 Blind Eye.m4a
-rw-rw-rw- 1 root root 10355301 Mar 10 2016 04 Echoes In The Dark.m4a
-rw-rw-rw- 1 root root 8087257 Mar 10 2016 05 Rain.m4a
-rw-rw-rw- 1 root root 9605474 Mar 10 2016 06 Sweet Lorraine.m4a
-rw-rw-rw- 1 root root 9141838 Mar 10 2016 07 Tales.m4a
-rw-rw-rw- 1 root root 22511187 Mar 10 2016 08 The Magician's Birthday.m4a
$ stat "07 Tales.m4a"
File: '07 Tales.m4a'
Size: 9141838 Blocks: 17856 IO Block: 4096 regular file
Device: 31h/49d Inode: 11 Links: 1
Access: (0666/-rw-rw-rw-) Uid: ( 0/ root) Gid: ( 0/ root)
Access: 2016-03-10 17:22:24.000000000 -0700
Modify: 2016-03-10 17:22:24.000000000 -0700
Change: 2016-03-10 17:22:24.000000000 -0700
Voila! I can now see the Last Access Date like my project needs. Unfortunately I discover Android has the biggest security hole in the history of Mankind. Although based on the Linux Kernel Google decided to disable the date a file was opened and read.
I welcome all comments / questions about this answer