Running the Sword, even if I was reluctant at first and still maybe am, is probably the right thing to do. If anything to let my players familiar themselves with how the game functions before delving into character burning, a pretty daunting task if every step of the burning introduces a new unfamiliar concept. Two of the three players are old d&d’ers and the third is pretty new to roleplaying but he too is fond of dungeons and crawling around in them, so Theolins Rift sounds interesting. Can you still get hold of it or is it suck in the adventure burner and lost to the shelves?
If your D&Ders are dungeoncrawlers, Torchbearer could be a good intro to how Burning Wheel works. This is how I came to it. Torchbearer, to me, is like “basic burning wheel”. Character creation is simple, beliefs are on rails and tied to the immediate dungeon/adventure etc.
The sword is a great adventure for BW because it highlights something that D&D can’t do, which is provide for meaningful non-lethal PvP between players. It puts social combat front and center with the belief system, showing that BW just isn’t a fiddly skill-based level-less d&d clone, but something more.
Looks like it’s lost to the shelves (I couldn’t find it when I looked anyways)
For what it’s worth, it doesn’t really require knowledge of the advanced mechanics to burn a character. Circles and Resources, for example, are derived from what you spent points on. Weapon stats are pretty easily explained and you can simply tell your player to take the weapon that their character would use and leave it at that. The real challenge is writing good, actionable Beliefs and useful instincts, which is why I think playing The Sword is useful. All of the characters have solid examples of both and understanding how those are used to drive play is more important than understand the other mechanics right away.