Rods could provide that, but they don't offer particularly great surface area characteristics, and they don't pack well together unless square or hexagonal in shape, and have "holding on to the candle when the wick reaches the bottom" problems.

Wire might work, but it doesn't make sense from a refueling standpoint, as you either need to maintain many small spools, or you need to eject a partially expended spool. Pure magnesium also has brittleness issues.

My most recent attempt at a solution is flat ticket-sized cards. They can be stacked together to form a tightly packed storage format, and popped off the stack to be fed into the burner.

Now that doesn't solve the burn-to-the-end problem on its own. But what if you cut a notch on each card and wedged the next card into it? With a system like that, you can theoretically make a train of fuel cards that can be long enough to keep the flame at a safe distance.

Depending on how the slotted-together cards are allowed to lay against each other, this could form a rough "X" or cross profile. That exposes a decent amount of surface area relative to mass, and depending on the cut pattern allow for some dimensional stability. A early test I did burning some cardboard slivers suggests it's at least worth continuing to chase down.