+2 on the Quill adapter. Your Burley is a nice bike, particularly at the price you paid, but it's not worth changing the whole front end.
You're talking a new tandem rated fork, new headset, and new stem. It could easily run you more than you paid for the bike, and won't accomplish much that the adapter wouldn't.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.