Configuration

Following these instructions and this answer and this document:

1. Do not execute the script shown in the question.
2. Edit /usr/share/X11/xorg.conf.d/10-evdev.conf.
3. Append the following lines:

   Section "InputClass"
       Identifier  "Marble Mouse"
       MatchProduct "Logitech USB Trackball"
       MatchIsPointer "on"
       MatchDevicePath "/dev/input/event*"
       Driver "evdev"
       Option "ButtonMapping" "1 9 3 4 5 6 7 8 2"
       Option "EmulateWheel" "true"
       Option "EmulateWheelButton" "8"
       Option "ZAxisMapping" "4 5"
       Option "XAxisMapping" "6 7"
       Option "Emulate3Buttons" "true"
   EndSection
   

4. Save and restart X.

Restart X

Enable Ctrl-Alt-Backspace to restart X as follows:

echo setxkbmap -option terminate:ctrl_alt_bksp >> ~/.xprofile
chmod +x ~/.xprofile
~/.xprofile

This:

1. Sets the small left button as the wheel activator (click and hold to scroll).
2. Sets the small left button as the "back button" (click, no scroll).
3. Sets the small right button as middle-click to paste.
4. Enables horizontal and vertical scrolling.
5. Disables both large buttons as chord-click.

Addendum

After rebooting restarting X, I found the scrolling no longer worked, possibly due to an upgrade. If this happens to you, try:

1. Remove the following files (I moved mine to ~/.):

   /usr/share/X11/xorg.conf.d/50-vmmouse.conf
   /usr/share/X11/xorg.conf.d/50-marblemouse.conf
   /usr/share/X11/xorg.conf.d/11-evdev-quirks.conf
   

2. Remove any additional mouse input device settings from:

   /etc/X11/xorg.conf
   

Verification

Verify the settings using (where 8 is the device number; yours will likely vary):

xinput get-button-map 8

"when I lock the screen, it behaves like something was pressing enter every ~500ms, so it's not possible to enter the password"

I was able to fix this by uninstalling lightdm and gdm3, and then reinstalling both, and running sudo dpkg-reconfigure lightdm which took me to a dialog where I chose lightdm over gdm3 (which was used before). Now I am at least able to lock and unlock the system. Still no Flashback though.