Drilling for methane adds GHGs to climate change.

For DRI, use a solar power tower to directly heat ore with "syngas" made similarly with solar heating and a renewable carbon source.

Such a setup can approach closed-loop production and emissions capture.

Sure. But we also can synthesize methane from captured carbon dioxide and green hydrogen. It's still more expensive than fossil methane, but it's getting cheaper.

But we can start transitioning factories to use methane right now, starting from fossil methane and slowly moving to greener sources.

You're suggesting unworkable processes that would take an absolute crapton of energy and be very expense.

Uhm... Which one? Reduction of iron ore with methane is energetically as good as anything else.

Synthetic methane is estimated right now to be about 2.5x the cost of fossil one when deployed at scale: https://www.sciencedirect.com/science/article/pii/S187551002...

This is pretty reasonable.

It's not particularly unlikely that we'll have to tear down or repurpose all that methane transportation infrastructure once we prioritize that global warming caused by leaks in that infrastructure.

Transporting ammonia doesn't have the leaks-make-global-warming problem