You can't actually get Everyone to have access to somebodies desktop because it is within a specific users profile. So somebody else logged into the local PC could access it, nobody outside of it on the LAN (the printer) should be able to.
So resolve that by putting the share on the root of the drive , share it again, but add the specific account that the printer will be using to the permissions and when you type in the username on the printer , be sure to add it how it displays in the folder within the brackets (As you know that was the solution in the post you referenced). Then right-click the folder and choose Send to > Desktop (Create shortcut).
That will resolve a ton of issues that can come up including when someone eventually accidentally moves/deletes the share. It also eliminates the possibility of someone else being able to access files within the local users profile.
Most likely your issue is simply that the folder is located within a users profile.