There’s a fourth option missing: a deeper physical theory may show the constants aren’t free parameters at all but are fixed by necessity. Wouldn’t that dissolve the problem without luck, multiverse, or design?

Many physicists do expect this, and it belongs on the list. The reply from design defenders is that a theory fixing the constants by necessity would itself be a remarkable fact requiring explanation: why should the only possible physics be life-permitting? On that view the fine-tuning relocates rather than vanishes. Whether that reply works is contested. Treat necessity as a live fourth option, and weigh the design proponent’s response to it alongside the other three.