"One note of caution that I heard is that the best way to attract a bear is to burn food."

well, maybe, if you load your canoe with sugar and burn it.  Doesn't seem like there would be much difference between burning the leftovers and cooking the same food originally  (mmmmn bacon).  In a hot fire, the leftovers would probably burn up pretty quickly - and compared to what, burying the leftovers - that would also likely attract bears if it wasn't buried good and deep.  I odn't normally have leftovers - if anything, it would be fish remnants from fish that was cooked over the fire - don't see that burning thr remains would make that big a difference.