I stumbled upon a relatively good magma-incinerator. It exploits the fact that you can pile up magma on top of magma, and can be thought of as a retracting bridge design without the retracting bridge.
Start with a large magma reservoir.
Build a smaller incineration chamber on top of the magma reservoir. The floor of the chamber should be downstairs or grates - downstairs generally work fine, but grates will catch falling objects if you're using a chute. To be clear, the downstairs are directly on top of magma. Dwarves walking across them will have magma right under their feet.
Build pumps which draw magma from the reservoir and into the left end of the incineration chamber.
When the pumps are switched on, the pumped magma will "float" across the magma in the reservoir below the downstairs/grates, burning everything on the downstairs/grates. Exactly how far the magma will travel depends on how effectively the pumps can draw magma - about 15 or 20 tiles seems doable for a simplistic setup. It also seems to depend on what direction the magma is flowing, it seems to work best if it flows from left to right, in the other direction it only seems to go a few tiles before sinking.
Once the pumps are switched off, the magma will, in a matter of seconds, sink down through the downstairs/grates back into the reservoir, allowing your dwarves to re-enter to dump refuse or collect iron - or to let the next squad of enemies in for processing.
So as I said it's like a retracting bridge design without the retracting bridge. The pump pressure alone is enough to keep the chamber flooded with magma. And it's quite a bit less effort to set up, requiring a mere fraction of the magma safe materials. (Incidentally I stumbled upon it by failing to use a magma safe retracting bridge. When the bridge melted, I noticed the chamber worked fine without the bridge, for as long as the pump was running).