In Service Desk 8.2 each request / ticket now has a permalink that can be seen at the bottom of the ticket details and easily copied to the clipboard. There's also an option when adding a note to automatically include the permalink as a part of the note.
Wow, I wish I had found that sooner. Thanks!!
Still, I think that the URLs which the system uses all the time should be those permalinks, or, at least there should be something in the UI of the ticket itself which makes this permalink evident/available to the user. That's a pretty common UI/UX convention now.