any steel plant that choses more expensive ingredients is going to quickly go out of business

That's true, and perhaps governments could/should kick in. The shift would be overall advantageous for society, so I think that it could be viable to tax coke production and use those taxes to subsidise plants using greener energy, offsetting the costs.

In the meantime, perhaps some global measures. Such as a treaty specifically addressing steel-based carbon emissions. Big thing here would be to convince the big three (China, India, and Japan); if the shift is desirable and viable for those three, others are easier to convince.