Can't Set Desktop Background in Fullscreen App

I'm late to the party, but this should work for you:

-- Set user_project_path to the folder that contains this AppleScript
set user_project_path to POSIX path of ((path to me as string) & "::")

-- Assuming your images are contained in user_project_path directory inside an images folder
set images_directory to user_project_path & "images/" as string

tell application "System Events"
  set desktopCount to count of desktops
  repeat with desktopNumber from 1 to desktopCount
    tell desktop desktopNumber
        -- Change my-desktop-image.png below to the name with extension of your desired image
        set picture to images_directory & "my-desktop-image.png"
    end tell
  end repeat
end tell

If you have questions, let me know