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.

However, that paper test did highlight that certain configurations could lead to uneven burning, which might compromise the whole slotted fuel concept altogether. Definitely needs more study.

Also need to investigate whether a feed mechanism from "stack" to card stream would be feasible to create, and whether one could operate at the rates needed to keep up with combustion.

@ACTupper Sounds exciting! You have thought about injecting the magnesium molten? 650° is a nice friendly melting point, unlike most of magnesium's other characteristics. Unwanted oxide deposits won't melt (under practically attainable conditions anyway) but do clean off with vinegar if not overheated.