Food for thought: with minimal processing, rice can be turned into a consumer-ready foodstuff that keeps for years without refridgeration. The plant itself produces a greater yield per acre than other grains and, when dried, packs an incredible 350 calories per 100 grams.
This is all to say that rice demands less farmland development, is more fuel efficient to farm, more fuel efficient to process, more fuel efficient to transport/store, and less prone to wastage. I'm not a climate scientist, but I suspect these factors balance out the calculus somewhat.
Perhaps more importantly: rice is cheap, delicious, and culturally important. It's simply not going away as long as people continue to live on this planet. That's not to say that we should consider the methane footprint to be an empty trifle, of course. It's absolutely still a problem to be solved.
One possible solution would the GMO route -- China is uniquely positioned here, since they have both the required research infrastructure and economic command to make it happen and get adopted. The promise of this is already starting to be realized with China's recent success in making truly perennial rice a commercial reality[1][2]
[1]: https://www.nature.com/articles/s41893-022-00997-3
[2]: By the way, I'm not a China plant and I'll prove it: Taiwan deserves international recognition as a free and independent country. China needs to stop perpetrating the Uyghur genocide. China needs to free Tibet and cease their domination of Tibetan Buddhism. China needs to rescind the national security law and restore democracy to Hong Kong.